Category Theory: TERMS

• Key concepts

  • object

  • morphism/arrow

  • category

  • category axioms

    • associativity of morphisms

    • identity morphism

  • commutative diagram

  • concrete category

  • CCC

  • functor

  • exponential

  • adjoint functors

  • end

  • kan extension

  • natural transformation

  • universal property

• Universal constructions

  • universal property

  • universal morphism

  • Limits

    • Terminal objects

    • Products

    • Equalizers

      • Kernels

    • Pullbacks

    • Inverse limit

  • Colimits

    • Initial objects

    • Coproducts

    • Coequalizers

      • Cokernels and quotients

    • Pushout

    • Direct limit

• Category theory

  • Higher Category Theory

  • Dependent Type Theory

  • Homotopy Type Theory

• Category types Kleisli category small category concrete category category of sets opposite category dual category comma category ordered category

• morphism, arrow

  • isomorphism

  • homomorphism

  • automorphism

  • endomorphism (identity-like)

• objects

  • initial object

  • terminal object

  • free object

• Misc

  • direct product

  • direct sum

  • free group

  • free lattice

  • Grothendieck group

  • Dedekind-MacNeille completion

  • product topology

  • Stone-Čech compactification

  • tensor product

  • inverse limit

  • direct limit

  • kernel

  • cokernel

  • pullback

  • pushout

  • equalizer

  • object precedence

  • concretizable vs non-concretizable

  • functors

  • functor

  • faithful functor

  • forgetful functor

  • adjunction

  • monad

  • universal property

  • universal morphism

  • universal construction

  • natural transformation