-
Notifications
You must be signed in to change notification settings - Fork 22
/
papers.bib
1652 lines (1482 loc) · 50.7 KB
/
papers.bib
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
@Misc{Clinton-is-is,
author = {Clinton, Bill},
title = {That depends on what the definition of "is" is.},
howpublished = {Interview}
}
@Misc{VV-IHP-talk,
author = {Voevodsky, Vladimir},
year = {2014},
title = {Univalent Foundations - new type-theoretic foundations of mathematics},
howpublished = {{s}lides from a talk at IHP, Paris, on April 22, 2014,
available at \url{https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2014_04_22_slides.pdf}}}
@Misc{VV-resizing,
author = {Voevodsky, Vladimir},
year = {2011},
title = {{Resizing Rules - their use and semantic justification}},
howpublished = {{s}lides from a talk available at \url{https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2011_Bergen.pdf}}}
@Misc{Swansea-Shulman,
author = {Shulman, Michael},
year = {2012},
title = {{Minicourse on Homotopy Type Theory}},
howpublished = {{slides from a talk, available} at \url{http://home.sandiego.edu/~shulman/hottminicourse2012/}}}
@Misc{Foundations,
AUTHOR = {Voevodsky, Vladimir},
title = {{Foundations: Development of the univalent foundations of mathematics in Coq}},
howpublished = {a Coq library of formalized proofs, available at \url{https://github.com/vladimirias/Foundations}}
}
@Misc{UniMath,
author = {Voevodsky, Vladimir and Ahrens, Benedikt and Grayson, Daniel and others},
title = {{UniMath --- a computer-checked library of univalent mathematics}},
howpublished = {{available} at \url{http://UniMath.org}}
}
@Misc{Lean,
title = {Lean theorem prover},
howpublished = {a proof assistant together with a library of formalized proofs, available at \url{https://github.com/leanprover/lean}}}
@Misc{RedPRL,
title = {{RedPRL}},
howpublished = {a proof assistant for Computational Cubical Type Theory together with a library of formalized proofs, available at \url{http://www.redprl.org/}}}
@Misc{HoTT,
title = {{The HoTT Library}},
howpublished = {a Coq library of formalized proofs, available at \url{https://github.com/HoTT/HoTT}}
}
@Misc{HoTT-Agda,
title = {{Homotopy Type Theory in Agda}},
howpublished = {an Agda library of formalized proofs, available at \url{https://github.com/HoTT/HoTT-Agda}}
}
@article {UniMath2015,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {An experimental library of formalized mathematics based on the
univalent foundations},
JOURNAL = {Math. Structures Comput. Sci.},
FJOURNAL = {Mathematical Structures in Computer Science. A Journal in the
Applications of Categorical, Algebraic and Geometric Methods
in Computer Science},
VOLUME = {25},
YEAR = {2015},
NUMBER = {5},
PAGES = {1278--1294},
ISSN = {0960-1295},
MRCLASS = {68N18 (03B35)},
MRNUMBER = {3340542},
DOI = {10.1017/S0960129514000577},
URL = {http://dx.doi.org/10.1017/S0960129514000577},
}
@inproceedings {MR0387023,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {Hauptsatz for the intuitionistic theory of iterated inductive
definitions},
BOOKTITLE = {Proceedings of the {S}econd {S}candinavian {L}ogic {S}ymposium
({U}niv. {O}slo, {O}slo, 1970)},
PAGES = {179--216. Studies in Logic and the Foundations of Mathematics,
Vol. 63},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1971},
MRCLASS = {02D99 (02C15)},
MRNUMBER = {0387023 (52 \#7870)},
MRREVIEWER = {Horst Luckhardt},
}
@incollection {MR0387009,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {An intuitionistic theory of types: predicative part},
BOOKTITLE = {Logic {C}olloquium '73 ({B}ristol, 1973)},
PAGES = {73--118. Studies in Logic and the Foundations of Mathematics,
Vol. 80},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1975},
MRCLASS = {02C15 (02D99)},
MRNUMBER = {0387009 (52 \#7856)},
MRREVIEWER = {Horst Luckhardt},
}
@incollection {39,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Subsystems and regular quotients of {C}-systems},
BOOKTITLE = {A panorama of mathematics: pure and applied; Conference on Mathematics and its Applications, (Kuwait City, 2014)},
SERIES = {Contemp. Math.},
VOLUME = {658},
PAGES = {127--137},
PUBLISHER = {Amer. Math. Soc., Providence, RI},
YEAR = {2016},
MRCLASS = {03B15 (03B22 03F50 03G25)},
MRNUMBER = {3475277},
MRREVIEWER = {Krzysztof R. Kapulkin},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1090/conm/658/13124},
}
@Misc {mcall,
AUTHOR = {McAllester, David},
TITLE = {Morphoid Type Theory, A Typed Platonic Foundation for Mathematics},
note = {\arxiv{1407.7274}}
}
@Misc {42,
title = {C-system of a module over a monad on sets},
year = {2014},
author = {Voevodsky, Vladimir},
note = {\arxiv{1407.3394}}
}
@Misc {40,
title = {B-systems},
year = {2014},
note = {\arxiv{1410.5389}},
author = {Voevodsky, Vladimir}
}
@Misc {104,
title = {Products of families of types in the {C}-systems defined by a universe category},
year = {2015},
note = {\arxiv{1503.07072}},
author = {Voevodsky, Vladimir}
}
@Misc {103,
title = {Martin-{L}\"of identity types in the {C}-systems defined by a universe category},
year = {2015},
pages = {1--51},
note = {\arxiv{1505.06446}},
author = {Voevodsky, Vladimir}
}
@article {109,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {A {C}-system defined by a universe category},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {30},
YEAR = {2015},
number = {37},
PAGES = {1181--1215},
note = {\arxiv{1409.7925}},
ISSN = {1201-561X},
MRCLASS = {18Cxx (03G30)},
MRNUMBER = {3402489},
url = {http://www.tac.mta.ca/tac/volumes/30/37/30-37.pdf}
}
@article {110,
title = {Lawvere theories and {J}f-relative monads},
journal = {arXiv:1601.02158},
year = {2016},
pages = {1--21},
note = {\arxiv{1601.02158}},
author = {Voevodsky, Vladimir}
}
@article {112,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Products of families of types and {$(\Pi,\lambda)$}-structures
on {C}-systems},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {31},
YEAR = {2016},
PAGES = {Paper No. 36, 1044--1094},
ISSN = {1201-561X},
MRCLASS = {03F50 (03B15 18C50 18D15)},
MRNUMBER = {3584698},
url = {http://www.tac.mta.ca/tac/volumes/31/36/31-36.pdf},
MRREVIEWER = {Thomas Streicher},
}
@article {MR3607210,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {The {$(\Pi, \lambda)$}-structures on the {C}-systems defined
by universe categories},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {32},
YEAR = {2017},
PAGES = {Paper No. 4, 113--121},
ISSN = {1201-561X},
MRCLASS = {18C50 (03B15 03F50 18D15)},
MRNUMBER = {3607210},
MRREVIEWER = {Thomas Streicher},
}
@article {MR3607209,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {C-systems defined by universe categories: presheaves},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {32},
YEAR = {2017},
PAGES = {Paper No. 3, 53--112},
ISSN = {1201-561X},
MRCLASS = {18D15 (03F50)},
MRNUMBER = {3607209},
}
@Misc{1211.2851,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu},
Title = {The {S}implicial {M}odel of {U}nivalent {F}oundations (after {V}oevodsky)},
Year = {2012},
note = {\arxiv{1211.2851}}
}
@Misc{1203.2553,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu and Voevodsky, Vladimir},
Title = {Univalence in Simplicial Sets},
Year = {2012},
note = {\arxiv{1203.2553}}
}
@Book{peano-principia,
author = {Peano, Giuseppe},
title = {Arithmetices principia: nova methodo},
publisher = {Fratres Bocca},
year = 1889,
url = {https://books.google.com/books?id=z80GAAAAYAAJ},
note = {See also \url{https://github.com/mdnahas/Peano_Book/} for a parallel translation by Vincent Verheyen}
}
@Book{hottbook,
author = {The {Univalent Foundations Program}},
title = {Homotopy Type Theory: Univalent Foundations of Mathematics},
publisher = {\url{https://homotopytypetheory.org/book}},
address = {Institute for Advanced Study},
year = 2013}
@Book{constructive-algebra,
author = {Mines, Ray and Richman, Fred and Ruitenburg Wim},
title = {A Course in Constructive Algebra},
publisher = {Springer-Verlag},
note = {Relevant Exercise 5 on page 133},
year = 1988}
@article {AwodeyBauer_prop_as_types,
AUTHOR = {Awodey, Steven and Bauer, Andrej},
TITLE = {Propositions as [types]},
JOURNAL = {J. Logic Comput.},
FJOURNAL = {Journal of Logic and Computation},
VOLUME = {14},
YEAR = {2004},
NUMBER = {4},
PAGES = {447--471},
ISSN = {0955-792X},
MRCLASS = {03B15 (03B20 03B45 18C50)},
MRNUMBER = {2081047},
DOI = {10.1093/logcom/14.4.447},
URL = {http://dx.doi.org/10.1093/logcom/14.4.447},
}
@incollection {MLTT79,
AUTHOR = {Martin-L\"of, Per},
TITLE = {Constructive mathematics and computer programming},
BOOKTITLE = {Logic, methodology and philosophy of science, {VI}
({H}annover, 1979)},
SERIES = {Stud. Logic Found. Math.},
VOLUME = {104},
PAGES = {153--175},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1982},
MRCLASS = {03F50 (03B70 03F55 68Q45)},
MRNUMBER = {682410},
MRREVIEWER = {B. H. Mayoh},
DOI = {10.1016/S0049-237X(09)70189-2},
URL = {http://dx.doi.org/10.1016/S0049-237X(09)70189-2},
}
@incollection {MR1678360,
AUTHOR = {Makkai, M.},
TITLE = {Towards a categorical foundation of mathematics},
BOOKTITLE = {Logic {C}olloquium '95 ({H}aifa)},
SERIES = {Lecture Notes Logic},
VOLUME = {11},
PAGES = {153--190},
PUBLISHER = {Springer, Berlin},
YEAR = {1998},
MRCLASS = {03B15 (00A30 03A05 03G30 18A15 18D05)},
MRNUMBER = {1678360},
MRREVIEWER = {Peter Johnstone},
DOI = {10.1007/978-3-662-22108-2_11},
URL = {http://dx.doi.org/10.1007/978-3-662-22108-2_11},
}
@article {MR2463991,
AUTHOR = {Gonthier, Georges},
TITLE = {Formal proof---the four-color theorem},
JOURNAL = {Notices Amer. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical Society},
VOLUME = {55},
YEAR = {2008},
NUMBER = {11},
PAGES = {1382--1393},
ISSN = {0002-9920},
MRCLASS = {05C15 (68T15)},
MRNUMBER = {2463991},
MRREVIEWER = {Solomon Marcus},
}
@article {MR1506041,
AUTHOR = {Russell, Bertrand},
TITLE = {Mathematical {L}ogic as {B}ased on the {T}heory of {T}ypes},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {30},
YEAR = {1908},
NUMBER = {3},
PAGES = {222--262},
ISSN = {0002-9327},
MRCLASS = {DML},
MRNUMBER = {1506041},
DOI = {10.2307/2369948},
URL = {http://dx.doi.org/10.2307/2369948},
}
@book {russell-intro-mp,
AUTHOR = {Russell, Bertrand},
TITLE = {Introduction to mathematical philosophy},
EDITION = {2\nd Ed.},
PUBLISHER = {Dover Publications, Inc., New York},
YEAR = {1993},
PAGES = {viii+208},
}
@article {bernays-7,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {VII}},
JOURNAL = {J. Symb. Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {19},
YEAR = {1954},
PAGES = {81--96},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0066320},
MRREVIEWER = {O. Frink},
}
@article {bernays-6,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {VI}},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {13},
YEAR = {1948},
PAGES = {65--79},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0025421},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2267328},
URL = {http://dx.doi.org/10.2307/2267328},
}
@article {bernays-5,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {V}. {G}eneral set theory},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {8},
YEAR = {1943},
PAGES = {89--106},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0009761},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2271051},
URL = {http://dx.doi.org/10.2307/2271051},
}
@article {bernays-4,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {7},
YEAR = {1942},
PAGES = {133--145},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0007731},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2268110},
URL = {http://dx.doi.org/10.2307/2268110},
}
@article {bernays-3,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {III}. {I}nfinity and
enumerability. {A}nalysis},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {7},
YEAR = {1942},
PAGES = {65--89},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0006333},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2266303},
URL = {http://dx.doi.org/10.2307/2266303},
}
@article {bernays-2,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {P}art {II}},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {6},
YEAR = {1941},
PAGES = {1--17},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0003382},
MRREVIEWER = {H. B. Curry},
DOI = {10.2307/2267281},
URL = {http://dx.doi.org/10.2307/2267281},
}
@article {bernays-1,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {P}art {I}},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {2},
YEAR = {1937},
PAGES = {65--77},
DOI = {10.2307/2268862},
http = {URL://dx.doi.org/10.2307/2268862},
}
@Misc{Coq,
author = {The {Coq Development Team}},
title = {The Coq Proof Assistant},
howpublished = {Available at \url{https://coq.inria.fr/}}
}
@Misc{1610.04591,
Author = {Bauer, Andrej and Gross, Jason and Lumsdaine, Peter LeFanu and Shulman, Mike and Sozeau, Matthieu and Spitters, Bas},
Title = {{The HoTT Library: A formalization of homotopy type theory in Coq}},
Year = {2016},
note = {\arxiv{1610.04591}},
}
@article {IMGelfand,
AUTHOR = {Beilinson, A.},
TITLE = {I. {M}. {G}elfand and his seminar---a presence},
JOURNAL = {Notices Amer. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical Society},
VOLUME = {63},
YEAR = {2016},
NUMBER = {3},
PAGES = {295--298},
ISSN = {0002-9920},
note = {\arxiv{1505.00710}},
MRCLASS = {01A70},
MRNUMBER = {3445168},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1090/noti1337},
}
@Misc{1605.03227,
Author = {Hou, Kuen-Bang Hou (Favonia) and Finster, Eric and Licata, Dan and Lumsdaine, Peter LeFanu},
Title = {{A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory}},
Year = {2016},
note = {\arxiv{1605.03227}},
}
@Misc{RezkBM,
Author = {Rezk, Charles},
Title = {{Proof of the Blakers-Massey Theorem}},
note = {Available at \url{https://faculty.math.illinois.edu/~rezk/freudenthal-and-blakers-massey.pdf}},
}
@Misc{1703.09050,
Author = {Anel, Mathieu and Biedermann, Georg and Finster, Eric and Joyal, Andr\'e},
Title = {{A Generalized Blakers-Massey Theorem}},
Year = {2017},
note = {\arxiv{1703.09050}},
}
@Misc{1703.09632,
Author = {Anel, Mathieu and Biedermann, Georg and Finster, Eric and Joyal, Andr\'e},
Title = {{Goodwillie's Calculus of Functors and Higher Topos Theory}},
Year = {2017},
note = {\arxiv{1703.09632}},
}
@Misc{1709.09519,
Author = {Kapulkin, Chris and Szumiło, Karol},
Title = {{Internal Language of Finitely Complete $(\infty,1)$-categories}},
Year = {2017},
note = {\arxiv{1709.09519}},
}
@Misc{1610.00037,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu},
Title = {{The homotopy theory of type theories}},
Year = {2016},
note = {\arxiv{1610.00037}},
}
@Misc{1606.05916,
Author = {Brunerie, Guillaume},
Title = {{On the homotopy groups of spheres in homotopy type theory}},
Year = {2016},
note = {{Ph.D.} thesis, \arxiv{1606.05916}},
}
@Misc{1710.10307,
Author = {Brunerie, Guillaume},
Title = {{The James construction and $\pi_4(\mathbb{S}^3)$ in homotopy type theory}},
Year = {2017},
note = {\arxiv{1710.10307}, accepted for publication in the Journal of Automated Reasoning},
}
@Misc{cubicaltt,
author = {Cohen, Cyril and Coquand, Thierry and Huber, Simon and M\"ortberg, Anders},
howpublished = {the proof assistant {\tt cubical}, written in Haskell, available at \url{https://github.com/mortberg/cubicaltt}},
title = {Experimental implementation of Cubical Type Theory}
}
@article{1611.02108,
author = {Cohen, Cyril and Coquand, Thierry and Huber, Simon and M\"ortberg, Anders},
title = {{Cubical Type Theory: a constructive interpretation of the univalence axiom}},
note = {To appear in the post-proceedings of TYPES 2015. Preprint avaiable at https://arxiv.org/abs/1611.02108},
year = 2015,
}
@Misc{1705.07088,
Author = {Lumsdaine, Peter LeFanu and Shulman, Mike},
Title = {{Semantics of higher inductive types}},
Year = {2017},
note = {\arxiv{1705.07088}},
}
@Misc{1703.03007,
Author = {Shulman, Michael},
Title = {{Homotopy type theory: the logic of space}},
Year = {2017},
note = {\arxiv{1703.03007}},
}
@InCollection{Shulman-synthetic,
author = {Shulman, Michael},
title = {Homotopy type theory: a synthetic approach to higher
equalities},
booktitle = {Categories for the working philosopher},
pages = {36--57},
publisher = {Oxford Univ. Press, Oxford},
year = {2017},
eprint = {1601.05035},
eprinttype = {arxiv}
}
@article {0709.0248,
AUTHOR = {Awodey, Steve and Warren, Michael A.},
TITLE = {Homotopy theoretic models of identity types},
JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
Society},
VOLUME = {146},
YEAR = {2009},
NUMBER = {1},
PAGES = {45--55},
ISSN = {0305-0041},
MRCLASS = {03B15 (03B35 18G99 55U35)},
MRNUMBER = {2461866},
note = {\arxiv{0709.0248}},
MRREVIEWER = {Richard F. Blute},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1017/S0305004108001783},
}
@Article{ Shulman-Real-Cohesive,
title = {Brouwer's fixed-point theorem in real-cohesive homotopy
type theory},
volume = {28},
doi = {10.1017/S0960129517000147},
number = {6},
journal = {Mathematical Structures in Computer Science},
publisher = {Cambridge University Press},
author = {Shulman, Michael},
year = {2018},
pages = {856–941},
eprint = {1509.07584},
eprinttype = {arXiv}
}
@incollection {MR0274219,
AUTHOR = {de Bruijn, N. G.},
TITLE = {The mathematical language {AUTOMATH}, its usage, and some of
its extensions},
BOOKTITLE = {Symposium on {A}utomatic {D}emonstration ({V}ersailles, 1968)},
PAGES = {29--61},
PUBLISHER = {Lecture Notes in Mathematics, Vol. 125. Springer, Berlin},
YEAR = {1970},
MRCLASS = {94.40},
MRNUMBER = {0274219},
MRREVIEWER = {T. Rus},
}
@article {MR3363596,
AUTHOR = {Coquand, Thierry},
TITLE = {Th\'eorie des types d\'ependants et axiome d'univalence},
JOURNAL = {Ast\'erisque},
FJOURNAL = {Ast\'erisque},
NUMBER = {367-368},
YEAR = {2015},
PAGES = {Exp. No. 1085, x, 367--386},
ISSN = {0303-1179},
ISBN = {978-2-85629-804-6},
MRCLASS = {03B15 (18B40 55U40)},
MRNUMBER = {3363596},
MRREVIEWER = {Luca Paolini},
}
@incollection {MR3566711,
AUTHOR = {Hou, Kuen-Bang and Shulman, Michael},
TITLE = {The {S}eifert--van {K}ampen theorem in homotopy type theory},
BOOKTITLE = {Computer science logic 2016},
SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
VOLUME = {62},
PAGES = {Art. No. 22, 16},
PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
YEAR = {2016},
MRCLASS = {55U35 (03B40 18G30 68N18)},
MRNUMBER = {3566711},
}
@article {MR3340533,
AUTHOR = {Ahrens, Benedikt and Kapulkin, Krzysztof and Shulman, Michael},
TITLE = {Univalent categories and the {R}ezk completion},
JOURNAL = {Math. Structures Comput. Sci.},
FJOURNAL = {Mathematical Structures in Computer Science. A Journal in the
Applications of Categorical, Algebraic and Geometric Methods
in Computer Science},
VOLUME = {25},
YEAR = {2015},
NUMBER = {5},
PAGES = {1010--1039},
ISSN = {0960-1295},
MRCLASS = {18B99 (03B15)},
MRNUMBER = {3340533},
MRREVIEWER = {Thomas Streicher},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1017/S0960129514000486},
}
@incollection {MR3323808,
AUTHOR = {Licata, Daniel R. and Shulman, Michael},
TITLE = {Calculating the fundamental group of the circle in homotopy
type theory},
BOOKTITLE = {2013 28th {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in
{C}omputer {S}cience ({LICS} 2013)},
PAGES = {223--232},
PUBLISHER = {IEEE Computer Soc., Los Alamitos, CA},
YEAR = {2013},
MRCLASS = {03B15 (55U40)},
MRNUMBER = {3323808},
MRREVIEWER = {Thomas John Hunter},
}
@incollection {MR3281415,
AUTHOR = {Bezem, Marc and Coquand, Thierry and Huber, Simon},
TITLE = {A model of type theory in cubical sets},
BOOKTITLE = {19th {I}nternational {C}onference on {T}ypes for {P}roofs and
{P}rograms},
SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
VOLUME = {26},
PAGES = {107--128},
PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
YEAR = {2014},
MRCLASS = {03B15},
MRNUMBER = {3281415},
}
@Article{ Tsem1,
author = "Tsementzis, D.",
title = "Univalent foundations as structuralist foundations",
journal = "Synthese",
year = "2017",
month = "Sep",
day = "01",
volume = "194",
number = "9",
pages = "3583--3617",
doi = "10.1007/s11229-016-1109-x"
}
@article{Tsem2,
author = {Tsementzis, D.},
title = {What is a Higher-Level Set?†},
journal = {Philosophia Mathematica},
note= {(forthcoming), {Available at \url{https://academic.oup.com/philmat/article-abstract/2895117/What-is-a-Higher-Level-Set}}},
volume = {},
number = {},
pages = {},
year = {2017},
doi = {10.1093/philmat/nkw032},
URL = { + http://dx.doi.org/10.1093/philmat/nkw032},
eprint = {/oup/backfile/content_public/journal/philmat/pap/10.1093_philmat_nkw032/2/nkw032.pdf},
}
@article{Tsem3,
title={Foundations and Philosophy},
author={Tsementzis, D. and Halvorson, H.},
journal={Philosopher's Imprint (forthcoming)},
note={Available at \url{http://philsci-archive.pitt.edu/13504/}},
year={2017}
}
@article{Tsem4,
title={A Meaning Explanation for HoTT},
author={Tsementzis, D.},
note={Available at \url{http://philsci-archive.pitt.edu/12824/}},
year={2016}
}
@Misc {harper-et-al-1,
AUTHOR = {Angiuli, Carlo and Harper, Robert and Wilson, Todd},
TITLE = {{Computational higher type theory I: Abstract cubical realizability}},
year = {2016},
note = {\arxiv{1604.08873}}
}
@Misc {harper-et-al-2,
AUTHOR = {Angiuli, Carlo and Harper, Robert},
TITLE = {{Computational higher type theory II: Dependent cubical realizability}},
year = {2016},
note = {\arxiv{1606.09638}}
}
@Misc {harper-et-al-3,
AUTHOR = {Angiuli, Carlo and Hou, Kuen-Bang and Harper, Robert},
TITLE = {{Computational Higher Type Theory III: Univalent Universes and Exact Equality}},
year = {2017},
note = {\arxiv{1712.01800}}
}
@Misc {harper-et-al-4,
AUTHOR = {Cavallo, Evan and Harper, Robert},
TITLE = {{Computational Higher Type Theory IV: Inductive Types}},
year = {2018},
note = {\arxiv{1801.01568}}
}
@Misc {cart-cube,
author = {Angiuli, Carlo and Brunerie, Guillaume and Coquand, Thierry and Hou, Kuen-Bang and Harper, Robert and Licata, Daniel R.},
title = {{Cartesian Cubical Type Theory}},
year = {2017},
note = {{a}vailable at \url{https://github.com/dlicata335/cart-cube/raw/master/cart-cube.pdf}}}
@article{10.2307/986491,
ISSN = {0003049X},
URL = {http://www.jstor.org/stable/986491},
author = {Kenneth I. Appel},
journal = {Proceedings of the American Philosophical Society},
number = {1},
pages = {35-39},
publisher = {American Philosophical Society},
title = {The Use of the Computer in the Proof of the Four Color Theorem},
volume = {128},
year = {1984}
}
@article {MR0543793,
AUTHOR = {Appel, K. and Haken, W. and Koch, J.},
TITLE = {Every planar map is four colorable. {II}. {R}educibility},
JOURNAL = {Illinois J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {21},
YEAR = {1977},
NUMBER = {3},
PAGES = {491--567},
ISSN = {0019-2082},
MRCLASS = {05C15},
MRNUMBER = {0543793},
MRREVIEWER = {Frank Allaire},
URL = {http://projecteuclid.org/euclid.ijm/1256049012},
}
@article {MR0543792,
AUTHOR = {Appel, K. and Haken, W.},
TITLE = {Every planar map is four colorable. {I}. {D}ischarging},
JOURNAL = {Illinois J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {21},
YEAR = {1977},
NUMBER = {3},
PAGES = {429--490},
ISSN = {0019-2082},
MRCLASS = {05C15},
MRNUMBER = {0543792},
MRREVIEWER = {Frank Allaire},
URL = {http://projecteuclid.org/euclid.ijm/1256049011},
}
@InProceedings{10.1007/978-3-642-39634-2_14,
author="Gonthier, Georges
and Asperti, Andrea
and Avigad, Jeremy
and Bertot, Yves
and Cohen, Cyril
and Garillot, Fran{\c{c}}ois
and Le Roux, St{\'e}phane
and Mahboubi, Assia
and O'Connor, Russell
and Ould Biha, Sidi
and Pasca, Ioana
and Rideau, Laurence
and Solovyev, Alexey
and Tassi, Enrico
and Th{\'e}ry, Laurent",
editor="Blazy, Sandrine
and Paulin-Mohring, Christine
and Pichardie, David",
title="A Machine-Checked Proof of the Odd Order Theorem",
booktitle="Interactive Theorem Proving",
year="2013",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="163--179",
abstract="This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries of formalized mathematics, including results in finite group theory, linear algebra, Galois theory, and the theories of the real and complex algebraic numbers.",
isbn="978-3-642-39634-2"
}
@article{kepler,
title={{A formal proof of the Kepler conjecture}},
volume={5}, DOI={10.1017/fmp.2017.1}, journal={Forum of Mathematics, Pi}, publisher={Cambridge University Press},
author={Hales, Thomas and Adams, Mark and Bauer, Gertrud and Dang, Dat Tat and Harrison, John and Hoang, Truong Le and Kaliszyk, Cezary and Magron, Victor and Mclaughlin, Sean and Nguyen, Thang Tat and others},
year={2017},
pages={e2}
}
@InProceedings{CPP16p122,
author = {van Doorn, Floris},
title = {{Constructing the Propositional Truncation using Non-recursive HITs}},
booktitle = {Proc.\ Certified Proofs and Programs (CPP), 2016},
publisher = {ACM},
pages = {122--129},
doi = {10.1145/2854065.2854076},
year = {2016},
note = {\arxiv{1512.02274}}
}
@Misc{1802.01170,
title = {{On Higher Inductive Types in Cubical Type Theory}},
author = {Thierry, Coquand and Huber, Simon and M\"ortberg, Anders},
year = {2018},
note = {\arxiv{1802.01170}}}
@Misc{1802.02191,
title = {{Cellular Cohomology in Homotopy Type Theory}},
author = {Buchholtz, Ulrik and Hou, Kuen-Bang (Favonia)},
year = {February, 2018},
note = {\arxiv{1802.02191}}}
@Unpublished{ BCFR,
Author = {Buchholtz, Ulrik and Christensen, J. Daniel and Flaten, Jarl
G. Taxerås and Rijke, Egbert},
Title = {Central {H}-spaces and banded types},
ArchivePrefix ={arXiv},
EPrint = {2301.02636},
Year = 2023
}
@article{Kleiner-group-survey,
AUTHOR = {Kleiner, Israel},
TITLE = {The evolution of group theory: a brief survey},
JOURNAL = {Math. Mag.},
FJOURNAL = {Mathematics Magazine},
VOLUME = {59},
YEAR = {1986},
NUMBER = {4},
PAGES = {195--215},
DOI = {10.2307/2690312}
}
@article{Hawkins-Klein-EP,
AUTHOR = {Hawkins, Thomas},
TITLE = {The {\it {E}rlanger {P}rogramm} of {F}elix {K}lein:
reflections on its place in the history of mathematics},
JOURNAL = {Historia Math.},
FJOURNAL = {Historia Mathematica},
VOLUME = {11},
YEAR = {1984},
NUMBER = {4},
PAGES = {442--470},
DOI = {10.1016/0315-0860(84)90028-4}
}
@article {Klein-EP-en,
AUTHOR = {Klein, Felix},
TITLE = {A comparative review of recent researches in geometry},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical Society},
VOLUME = {2},
YEAR = {1893},
NUMBER = {10},
PAGES = {215--249},
DOI = {10.1090/S0002-9904-1893-00147-X}
}
@article {Klein-EP-de,
AUTHOR = {Klein, Felix},
TITLE = {Vergleichende {B}etrachtungen \"{u}ber neuere geometrische
{F}orschungen},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {43},
YEAR = {1893},
NUMBER = {1},
PAGES = {63--100},
DOI = {10.1007/BF01446615},
langid = {ngerman}
}
@book{Wussing-genesis,
AUTHOR = {Wussing, Hans},
TITLE = {The genesis of the abstract group concept},
NOTE = {A contribution to the history of the origin of abstract group
theory,
Translated from the German by Abe Shenitzer and Hardy Grant},
PUBLISHER = {MIT Press, Cambridge, MA},
YEAR = {1984},
PAGES = {331}
}
@article{Le-premises,
AUTHOR = {L\^{e}, Fran\c{c}ois},
TITLE = {``{G}eometrical equations'': forgotten premises of {F}elix
{K}lein's {\it {E}rlanger {P}rogramm}},
JOURNAL = {Historia Math.},
FJOURNAL = {Historia Mathematica},
VOLUME = {42},
YEAR = {2015},
NUMBER = {3},
PAGES = {315--342},
DOI = {10.1016/j.hm.2014.11.002}
}
@Misc{circlerec-Dan,
author = {Grayson, Dan},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/master/UniMath/SyntheticHomotopyTheory/Circle.v}},
title = {The file containing the proof of circle recursion}
}
@Misc{circleind-Dan,
author = {Grayson, Dan},
title = {The file containing the proof of circle induction},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/master/UniMath/SyntheticHomotopyTheory/Circle2.v}},
}
@Misc{circleind-Dan-theorem,
author = {Grayson, Dan},
title = {The statement and proof of the circle induction theorem, a snapshot},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/d5e570ba972bca92ec6b9023e5166034b0d79654/UniMath/SyntheticHomotopyTheory/Circle2.v\#L268}},
}
@Misc{circleind-Mike,
author = {Shulman, Mike},
howpublished = {\url{https://groups.google.com/d/msg/homotopytypetheory/hE1eY-v_Kes/bdSoAxC9224J}},
title = {Proof sketch of circle induction}
}