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Qu'est-ce (qui) est oversaturated subcategory - définition
FULL SUBCATEGORY WHOSE INCLUSION FUNCTOR HAS A LEFT ADJOINT
Coreflective subcategory
Isomorphism-closed subcategory
A SUBCATEGORY THAT DOES NOT DISCRIMINATE BETWEEN ISOMORPHIC OBJECTS IN THE SUPERCATEGORY
Isomorphism-closed; Replete subcategory
In category theory, a branch of mathematics, a subcategory \mathcal{A} of a category \mathcal{B} is said to be isomorphism closed or replete if every \mathcal{B}-isomorphism h:A\to B with A\in\mathcal{A} belongs to \mathcal{A}. This implies that both B and h^{-1}:B\to A belong to \mathcal{A} as well.
Subcategory
IN MATHEMATICS, A CATEGORY, WHOSE OBJECTS AND MORPHISMS ARE INSIDE A BIGGER CATEGORY
Full subcategory; Subcategories; Inclusion functor; Strictly full subcategory; Full embedding; Full subcategories; Wide subcategory
In mathematics, specifically category theory, a subcategory of a category C is a category S whose objects are objects in C and whose morphisms are morphisms in C with the same identities and composition of morphisms. Intuitively, a subcategory of C is a category obtained from C by "removing" some of its objects and arrows.
subcategory
IN MATHEMATICS, A CATEGORY, WHOSE OBJECTS AND MORPHISMS ARE INSIDE A BIGGER CATEGORY
Full subcategory; Subcategories; Inclusion functor; Strictly full subcategory; Full embedding; Full subcategories; Wide subcategory
¦ noun (plural subcategories) a secondary or subordinate category.
Derivatives
subcategorization or subcategorisation noun
subcategorize or subcategorise verb
Wikipédia
Reflective subcategory
In mathematics, a full subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint.: 91 This adjoint is sometimes called a reflector, or localization. Dually, A is said to be coreflective in B when the inclusion functor has a right adjoint.
Informally, a reflector acts as a kind of completion operation. It adds in any "missing" pieces of the structure in such a way that reflecting it again has no further effect.
