nLab enriched category theory contents

enriched category theory

Background

• category theory

• monoidal category, closed monoidal category

• cosmos, multicategory, bicategory, double category, virtual double category

Basic concepts

• enriched category

• enriched functor, profunctor

• enriched natural transformation

• enriched adjoint functor

• enriched product category

• enriched functor category

Universal constructions

• weighted limit

• end, coend

Extra stuff, structure, property

• copowering (tensoring)

  powering (cotensoring)

• monoidal enriched category

  • cartesian closed enriched category

  • locally cartesian closed enriched category

Homotopical enrichment

• enriched homotopical category

• enriched model category

• model structure on homotopical presheaves