- category of spaces
- мат.категория пространств
English-Russian scientific dictionary. 2008.
category of spaces
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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 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 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 vector spaces — In mathematics, especially category theory, the category K Vect has all vector spaces over a fixed field K as objects and K linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since… … 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 metric spaces — The category Met, first considered by Isbell (1964), has metric spaces as objects and metric maps or short maps as morphisms. This is a category because the composition of two metric maps is again metric.The monomorphisms in Met are the injective … Wikipedia
Category of finite dimensional Hilbert spaces — In mathematics, the category FdHilb has all finite dimensional Hilbert spaces for objects and linear transformations between them. PropertiesThis category * is monoidal, * possesses finite biproducts, and * is dagger compact … Wikipedia
Category of being — In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply categories. To investigate the categories of being is to determine the most fundamental and the broadest classes of entities.… … 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 theory — noun A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them … Wiktionary
Homotopy category — In mathematics, a homotopy category is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions. The homotopy category of all topological spaces is often denoted hTop or Toph.Homotopy… … Wikipedia
