# Isomorphism-closed subcategory

A subcategory which is isomorphism-closed and full is called strictly full. In the case of full subcategories it is sufficient to check that every ${\displaystyle {\mathcal {B}}}$-object which is isomorphic to an ${\displaystyle {\mathcal {A}}}$-object is also an ${\displaystyle {\mathcal {A}}}$-object.
This condition is very natural. E.g. in the category of topological spaces one usually studies properties which are invariant under homeomorphisms – so called topological properties. Every topological property corresponds to a strictly full subcategory of ${\displaystyle {\mathbf {Top} }.}$