- full subcategory
- мат.полная подкатегория
English-Russian scientific dictionary. 2008.
full subcategory
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Subcategory — In mathematics, 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 … Wikipedia
Full and faithful functors — In category theory, a faithful functor (resp. a full functor) is a functor which is injective (resp. surjective) when restricted to each set of morphisms with a given source and target.Explicitly, let C and D be (locally small) categories and let … Wikipedia
Reflective subcategory — In mathematics, a 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. This adjoint is sometimes called a reflector. Dually, A is said to be coreflective in B when the inclusion… … Wikipedia
Isomorphism-closed subcategory — A subcategory mathcal{A} of a category mathcal{B} is said to be isomorphism closed or replete if every mathcal{B} isomorphism h:A o B with Ainmathcal{A} belongs to mathcal{A}. This implies that both B and h^{ 1}:B o A belong to mathcal{A} as well … Wikipedia
Exact category — In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and… … Wikipedia
Category of rings — In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (preserving the identity). Like many categories in mathematics, the category of rings is… … Wikipedia
Compactly generated space — In topology, a compactly generated space (or k space) is a topological space whose topology is coherent with the family of all compact subspaces. Specifically, a topological space X is compactly generated if it satisfies the following condition:… … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Category of topological spaces — In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again… … Wikipedia
Gluing axiom — In mathematics, the gluing axiom is introduced to define what a sheaf F on a topological space X must satisfy, given that it is a presheaf, which is by definition a contravariant functor : F : O ( X ) rarr; C to a category C which initially one… … Wikipedia
Sequential space — In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability. Sequential spaces are the most general class of spaces for which sequences suffice to determine the… … Wikipedia
