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.

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