Isomorphism-closed subcategory
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A subcategory 
of a category 
is said to be isomorphism-closed or replete if every -isomorphism 
with 
belongs to 
This implies that both B and 
belong to as well.
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 -object which is isomorphic to an -object is also an -object.
This condition is very natural. E.g in the category of topological spaces we usually study properties which are invariant under homeomorphisms - so called topological properties. Every topological property corresponds to a strictly full subcategory of 
This article incorporates material from Isomorphism-closed subcategory on PlanetMath, which is licensed under the GFDL.
