Isomorphism-closed subcategory

In category theory, a branch of mathematics, a subcategory

is said to be isomorphism closed or replete if every

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

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

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