cokernel pair (changes) in nLab

category theory

• category

• functor

• natural transformation

• Cat

• universal construction

  • representable functor

  • adjoint functor

  • limit/colimit

  • weighted limit

  • end/coend

  • Kan extension

• Yoneda lemma

• Isbell duality

• Grothendieck construction

• adjoint functor theorem

• monadicity theorem

• adjoint lifting theorem

• Tannaka duality

• Gabriel-Ulmer duality

• small object argument

• Freyd-Mitchell embedding theorem

• relation between type theory and category theory

• sheaf and topos theory

• enriched category theory

• higher category theory

• applications of (higher) category theory

limits and colimits

1-Categorical

• limit and colimit

  • limits and colimits by example

  • commutativity of limits and colimits

  • small limit

  • filtered colimit

    • directed colimit

      • sequential colimit

  • sifted colimit

  • connected limit, wide pullback

  • preserved limit, reflected limit, created limit

  • product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum

  • finite limit

    • exact functor

• Kan extension

  • Yoneda extension

• weighted limit

• end and coend

• fibered limit

2-Categorical

• 2-limit

  • inserter

  • isoinserter

  • equifier

  • inverter

  • PIE-limit

• 2-pullback, comma object

(∞,1)-Categorical

• (∞,1)-limit

  • (∞,1)-pullback

    • fiber sequence

Model-categorical

• homotopy Kan extension

• homotopy limit

  • homotopy product

  • homotopy equalizer

  • homotopy fiber

  • mapping cone

  • homotopy pullback

  • homotopy totalization

  • homotopy end

• homotopy colimit

  • homotopy coproduct

  • homotopy coequalizer

  • homotopy cofiber

  • mapping cocone

  • homotopy pushout

  • homotopy realization

  • homotopy coend