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hom-group (changes) in nLab

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Context

Category theory

category theory

Concepts

  • category

  • functor

  • natural transformation

  • Cat

Universal constructions

  • universal construction

    • representable functor

    • adjoint functor

    • limit/colimit

    • weighted limit

    • end/coend

    • Kan extension

Theorems

  • 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

Extensions

  • sheaf and topos theory

  • enriched category theory

  • higher category theory

Applications

  • applications of (higher) category theory

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Contents

  • Idea
  • Examples
  • Related concepts

Idea

A hom-object in the case of enrichment over groups (often: abelian groups for an Ab-enriched category).

Examples

  • The abelian hom-groups of the stable homotopy category are cohomology groups in Whitehead-generalized cohomology theories.

Related concepts

  • hom-set

  • additive category

Last revised on July 13, 2021 at 09:08:39. See the history of this page for a list of all contributions to it.

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