nLab
small groupoid

A small groupoid is a groupoid with a small set of objects, instead of a proper class. Hence a small groupoid is a small category that is also a groupoid

In plain groupoid theory (homotopy theory) smallness is usually the default meaning of “groupoid”. But if one thinks of groupoids as special cases of categories, and since for categories the default definition allows a proper class of objects, while otherwise one explicitly speaks of a small category, it does make sense to speak of “small groupoids” at times.

Last revised on July 28, 2018 at 08:22:39. See the history of this page for a list of all contributions to it.