A subcategory of a category is said to be isomorphism-closed if for any and a -isomorphism $\Map hAB$ , also the -object $B$ belongs to .

More simply: the subcategory contains with each object all isomorphic -objects.

Another name commonly used for isomorphism-closed subcategories is replete subcategory.

This condition is very natural. E.g in the category of topological spaces we usually study properties which are invariant under homeomorphisms - so called topological properties. Every topological property corresponds to a strictly full subcategory of $\Top$ .

A subcategory which is isomorphism-closed and full is called strictly full.