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Visualizing Category Cheatsheet

What is this?

This repository contains LaTeX code to generate a text and a poster containing the basic definitions of category theory expressed in a diagrammatic and visual way. The goal is to create a handy reference for anyone new to category theory.

Why?

Category theory can be quite abstract. Visual representations can make it easier to grasp the concepts. This project aims to provide a visual aid to complement more traditional textual explanations. Demo visualization

How to use:

  1. Clone the repository: 
    git clone [URL non valido rimosso]
  2. Install necessary LaTeX dependencies: Ensure you have a LaTeX distribution (like TeX Live or MikTeX) and any additional packages mentioned in the LaTeX files.
  3. Compile the LaTeX code: Use your preferred LaTeX compiler (e.g., pdflatex) to compile the .tex files.

Contributing:

Feel free to contribute to this project! Here are some ways you can help:

  • Add new diagrams: Create diagrams for additional concepts in category theory.
  • Improve existing diagrams: Suggest improvements to the clarity or accuracy of existing diagrams.
  • Add new examples: Provide concrete examples to illustrate the concepts.
  • Fix typos or errors: Help us maintain the accuracy of the content.

To contribute:

  1. Fork the repository.
  2. Create a new branch.
  3. Make your changes.
  4. Commit and push.
  5. Submit a pull request.

I'm open to any suggestions!

License: GNU LESSER GENERAL PUBLIC LICENSE

Acknowledgements:

[List any resources or people who have contributed to the project]

  • this Readme file has been generated with GeminiAI.

Future work:

  • Animations: Create animations to illustrate complex concepts.
  • Interactive elements: Develop interactive elements (e.g., using JavaScript) to allow users to explore the diagrams.
  • Multilingual support: Translate the content into other languages.

Let's make category theory more accessible together!

TODO (in italian)

TODO Forma

  • File "dispensa" contiene tutti i blocchi organizzati in sezioni e sottosezioni
  • File Poster. Organizza tutti i blocchi in poster. WARN: c'è incompatibilità tra beamer e standalone in windows 10

TODO Contenuto

  • Definizione base
  • Funtori
    • functordef
    • basicfunctorclassification
    • functorclassification_1
    • functorclassification_2
  • Trasformazioni Naturali
    • naturaltransfdef
    • naturaltransfdefcompositions
  • Aggiunzioni
  • Limiti
    • limitdef
    • limitbestiary
    • (limiti in set)
  • Classificazione dei morfismi
    • basicmorphismclassification
  • Yoneda e Hom Funtori
  • Curry e Cartesian Closedness
  • Siti
  • Fasci
  • Topos elementari

Prospettive Future

  • Varie dal corso di U.S.
    • Generalized geometries
    • Homotopoical Categories
    • Super Geometry