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!

Revised on April 22, 2017 05:46:14 by Urs Schreiber (92.218.150.85)