CT SUMMARY

Category theory

• Fundamentals

  • category

  • object

  • arrow

  • axioms

  • Representation

    • transitive closure

    • commutative diagram

    • diagram chasing

    • directed graph

• Essence

  • category

  • functor

  • natural transformation

• Types of objects

  • initial object

  • terminal object

• Types of morphisms

  • identity

  • non-identity

  • Hom-set

  • isomorphism

  • monic

  • epic

• Types of categories

  • empty

  • subcategory

    • full

    • faithful

  • singleton

  • walking element

  • walking arrow

  • walking category

• Types of functors

  • identity functor

  • constant functor

  • endofunctor

• Types of named categories

• Types of categorical constructions