Cats

These are my notes on category theory, they are based mainly on

• Bartosz Milewski - Category Theory I
• Riehl - Category Theory in Context
• Perrone - Notes on Category Theory with examples from basic mathematics

I've tried to condense the material as much as possible and to keep the notation consistent.

In case you find them useful or if you spot any mistake/inaccuracy please let me know.

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• Categories
  • Product Categories
  • Opposite Categories

• Functors
  • Hom Functors
  • Left Action Functor

• Universal Construction
  • Initial abd Terminal Objects
  • Products and Coproducts
  • Exponentials
  • Limits and Colimits

• Natural Transformations
  • Functor Category
  • Representable Functors
  • Horizontal Composition

• Yoneda Lemma
  • Yoneda Embedding
  • Yoneda Perspective

• Adjunctions

• Monads Comonads
  • Monads as Extensions of Spaces
  • Monads as Theories of Operations
  • Monads and Adjunctions

• String Diagrams
  • for Monads
  • for Adjunctions
  • for Compact Closed Categories