Isomorphism-closed subcategory

In category theory, a branch of mathematics, a subcategory formula_1 of a category formula_2 is said to be isomorphism closed or replete if every formula_2-isomorphism formula_4 with formula_5 belongs to formula_6 This implies that both formula_7 and formula_8 belong to formula_1 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 formula_2-object that is isomorphic to an formula_1-object is also an formula_1-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 formula_13