In category theory, a branch of mathematics, a subcategory A {\displaystyle {\mathcal {A}}} of a category B {\displaystyle {\mathcal {B}}} is said to be isomorphism closed or replete if every B {\displaystyle {\mathcal {B}}} -isomorphism h : A → B {\displaystyle h:A\to B} with A ∈ A {\displaystyle A\in {\mathcal {A}}} belongs to A. Wikipedia