- category of sets
- мат.категория множеств
English-Russian scientific dictionary. 2008.
category of sets
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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 (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 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 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 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 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 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 3 cable — Category 3 cable, commonly known as Cat 3, is an unshielded twisted pair (UTP) cable designed to reliably carry data up to 10 Mbit/s, with a possible bandwidth of 16 MHz. It is part of a family of copper cabling standards defined jointly by the… … 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 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 preordered sets — The category Ord has preordered sets as objects and monotonic functions as morphisms. This is a category because the composition of two monotonic functions is monotone.The monomorphisms in Ord are the injective monotonic functions.The empty set… … Wikipedia
