About: Isomorphism-closed subcategory

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In category theory, a branch of mathematics, a subcategory of a category is said to be isomorphism closed or replete if every -isomorphism with belongs to This implies that both and belong to 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 -object that is isomorphic to an -object is also an -object.

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  • In category theory, a branch of mathematics, a subcategory of a category is said to be isomorphism closed or replete if every -isomorphism with belongs to This implies that both and belong to 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 -object that is isomorphic to an -object is also an -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 (en)
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  • Isomorphism-closed subcategory (en)
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  • In category theory, a branch of mathematics, a subcategory of a category is said to be isomorphism closed or replete if every -isomorphism with belongs to This implies that both and belong to 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 -object that is isomorphic to an -object is also an -object. (en)
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  • Isomorphism-closed subcategory (en)
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