nLab
locally groupoidal 2-category

A 22-category is locally groupoidal if each of its hom-categories is a groupoid. In other words, a locally groupoidal 22-category is a (2,1)(2,1)-category.

As the concept of 22-category makes sense either strictly or weakly (as a bicategory), so a locally groupoidal 22-category might be either a locally groupoidal strict 22-category or a locally groupoidal bicategory. As for 22-categories in general, it is really the strictness of the functors between them that matters.

Created on June 3, 2009 01:09:01 by Toby Bartels (71.104.230.172)