📝§ Category Theory

• Category theory is all about morphisms, not objects

  • Category Theory is a theory of functors

• Category definition

• Set theory: functions

• Hom-set

• Category Theory: Isomorphism

• Category Theory: Monomorphism

• Category Theory: Epimorphism

• Thin Category—preorder isomorphism

• Monoid

• Initial/Terminal object

• Category Theory: Product

• Discrete category

• Functor

  • Endofunctor

  • Bifunctor

  • Contravariant Functor

  • Cat (category)—a category of functors

• Monoidal category (also called tensor category)

  • Cartesian monoidal category

  • Cocartesian monoidal category

• Category Theory: Function object

Resources:

• Milewski₂₀₁₆

• https://www.youtube.com/user/DrBartosz/playlists

• category theory on nLab—wiki skewed to category theory point of view