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category of morphisms

См. также в других словарях:

  • Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   Wikipedia

  • Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… …   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

  • 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

  • Category of sets — In mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose morphisms are all functions. It is the most basic and the most commonly used category in mathematics.Properties of the category of setsThe… …   Wikipedia

  • Category of topological vector spaces — In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear …   Wikipedia

  • Category of elements — In category theory, for every presheaf P inhat C := mathbf{Set}^{C^{op the category of elements mathbf{El}(P) of P is the category defined as follows: * its objects are pairs (A,a) where A is an object of C and ain P(A), * its morphisms (A,a) o… …   Wikipedia

  • Category of groups — In mathematics, the category Grp has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory.The monomorphisms in Grp are precisely the… …   Wikipedia

  • Category of relations — In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.A morphism (or arrow) R : A → B in this category is a relation between the sets A and B , so nowrap| R ⊆ A × B .The composition of two relations R …   Wikipedia

  • Category of manifolds — In mathematics, the category of manifolds, often denoted Man p , is the category whose objects are manifolds of smoothness class C p and whose morphisms are p times continuously differentiable maps. This is a category because the composition of… …   Wikipedia

  • Category of magmas — In mathematics, the category of magmas (see category, magma for definitions), denoted by Mag, has as objects sets with a binary operation, and morphisms given by homomorphisms of operations (in the universal algebra sense). The category Mag has… …   Wikipedia

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