Equivalence of categories Category (mathematics) Abelian category Category of abelian groups Category of small categories Category of sets Category (topology)

Dec 4th 2016

In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability

Dec 28th 2016

Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category

Apr 23rd 2017

specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms

Jan 29th 2017

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. The arrows or morphisms between

Jan 31st 2017

In mathematics, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory)

Feb 3rd 2017

The pregnancy category of a medication is an assessment of the risk of fetal injury due to the pharmaceutical, if it is used as directed by the mother

Apr 23rd 2017

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows

Mar 24th 2017

about category management in a retail context. For category management in a purchasing context, see Category management (purchasing). Category management

Dec 3rd 2016

In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all

Jun 10th 2016

In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms:

Apr 19th 2017

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general

Dec 26th 2016

confused with inner product. In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor ⊗ : C × C → C that is associative

Mar 21st 2017

including Infinity category Segal category Simplicially enriched category Topological category Complete Segal space model category Workshop of homotopy

Jan 2nd 2016

categories in mathematics, the category of rings is large, meaning that the class of all rings is proper. The category Ring is a concrete category meaning

Nov 2nd 2016

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'

Apr 3rd 2017

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

Apr 11th 2017

in category theory, a preadditive category is a category that is enriched over the monoidal category of abelian groups. In other words, the category C

Jan 9th 2017

In mathematics, the homotopy category is a category built from the category of topological spaces which in a sense identifies two spaces that have the

Oct 17th 2016

A Category A service is a Canadian specialty television channel which, as defined by the Canadian Radio-television and Telecommunications Commission, must

Jan 8th 2017

A syntactic category is a type of syntactic unit that theories of syntax assume. Word classes, largely corresponding to traditional parts of speech (e

Dec 21st 2014

In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable

Feb 22nd 2017

In mathematics, a complete category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C where

May 1st 2016

CategoryCategory 6 cable, commonly referred to as Cat 6, is a standardized twisted pair cable for Ethernet and other network physical layers that is backward compatible

Apr 22nd 2017

A Category B service (formerly Category 2 prior to September 1, 2011) is a Canadian specialty television channel which, as defined by the Canadian Radio-television

Apr 15th 2017

Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise

Jan 21st 2017

IUCN protected area categories, or IUCN protected area management categories, are categories used to classify protected areas in a system developed by

Oct 2nd 2016

In category theory, a 2-category is a category with "morphisms between morphisms"; that is, where each hom-set itself carries the structure of a category

Jun 28th 2016

In mathematics, a dagger category (also called involutive category or category with involution ) is a category equipped with a certain structure called

Apr 20th 2017

A grammatical category is a property of items within the grammar of a language; it has a number of possible values (sometimes called grammemes), which

Nov 1st 2016

derived category of an abelian category and the stable homotopy category of spectra (more generally, the homotopy category of a stable ∞-category), both

Mar 17th 2017

Duality (mathematics). In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties

Jul 22nd 2016

composition and fallacy of division. A category mistake, or category error, or categorical mistake, or mistake of category, is a semantic or ontological error

Mar 2nd 2017

Prisoner security categories in the United Kingdom are one of four classifications assigned to every adult prisoner for the purposes of assigning them

Apr 3rd 2017

In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to

Mar 8th 2016

Category utility is a measure of "category goodness" defined in Gluck & Corter (1985) and Corter & Gluck (1992). It attempts to maximize both the probability

Sep 26th 2016

In category theory, a category is considered Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally

Dec 28th 2016

The list of Category 5 Atlantic hurricanes encompasses 31 tropical cyclones that reached Category 5 strength on the Saffir–Simpson hurricane wind scale

Apr 24th 2017

In mathematics, especially in category theory, a closed monoidal category (also called a monoidal closed category) is a context where it is possible both

Dec 13th 2016

In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree-1 maps between them

Oct 21st 2016

Category 5 hurricanes are tropical cyclones that reach Category 5 intensity on the Saffir-Simpson Hurricane Scale. They are by definition the strongest

Jan 9th 2017

In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product"

Dec 29th 2016

In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms

Jun 5th 2016

– Category of sets – Concrete category – Category of vector spaces – Category of graded vector spaces – Category of chain complexes – Category of finite

Oct 11th 2016

Category 4 may refer to: Category 4 cable, a cable that consists of four unshielded twisted-pair wires Category 4 fireworks, British fireworks that are

May 6th 2016

In category theory, a branch of mathematics, a stable ∞-category is an ∞-category such that (i) It has a zero object. (ii) Every morphism in it admits

Jan 26th 2016

In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in

Mar 22nd 2016

a category (German: Categorie in the original or Kategorie in modern German) is a pure concept of the understanding (Verstand). A Kantian category is

Jan 16th 2017

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas

Jan 3rd 2017

In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels

Jan 29th 2017

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