Enriched category theory
Higher category theory
higher category theory
Extra properties and structure
A -enriched category , for Grpd (the category of groupoids), has for every ordered pair of objects a groupoid of morphisms between and . This hom-object is hence a hom-groupoid in this case.
For this reason such a category may be thought of as a locally groupoidal 2-category, or (2,1)-category.
For Grpd the hom-groupoids are the functor categories between two groupoids.
For any small category, the (2,1)-presheaf-category has as hom-groupoid the groupoid of pseudonatural transformations and modifications between the pseudo-functors .
Revised on September 14, 2010 16:48:49
by Toby Bartels