In category theory, a branch of mathematics, a subcategory of a category is said to be isomorphism closed or replete if every -isomorphism with belongs to  This implies that both and belong to as well.
A subcategory that is isomorphism closed and full is called strictly full. In the case of full subcategories it is sufficient to check that every -object that is isomorphic to an -object is also an -object.
This condition is very natural. For example, in the category of topological spaces one usually studies properties that are invariant under homeomorphisms—so-called topological properties. Every topological property corresponds to a strictly full subcategory of