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 itself, 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 .
Last revised on July 11, 2017 at 04:57:22. See the history of this page for a list of all contributions to it.