# nLab strictly full subcategory

A subcategory is strictly full if it is full and closed under isomorphism (i.e. replete).

Note that, as a condition on subcategories, being strictly full is a property that does not respect the principle of equivalence of category theory; however, seeing the full subcategory as a condition on objects, that condition is in accord with the principle of equivalence precisely when the full subcategory is strictly full!

• The Stacks Project, Definition 4.2.10 tag/001D

Last revised on September 17, 2022 at 16:26:39. See the history of this page for a list of all contributions to it.