In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function. Given a category C {\displaystyle...

Applied category theory Category of sets Concrete category Category of vector spaces Category of graded vector spaces Category of chain complexes Category of...

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

category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism...

function's domain that all map to some single given point Image (category theory) – term in category theoryPages displaying wikidata descriptions as a fallback...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In category theory, a small set is one in a fixed universe of sets (as the word universe is used in mathematics in general). Thus, the category of small...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of...

In mathematics, the Elementary Theory of the Category of Sets or ETCS is a set of axioms for set theory proposed by William Lawvere in 1964. Although it...

codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels are dual to the kernels of category theory, hence the name:...

William Benoit, image restoration theory (also known as image repair theory) outlines strategies that can be used to restore one's image in an event where...

In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...

In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection...

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

In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any...

small category to an abelian category are abelian as well. These stability properties make them inevitable in homological algebra and beyond; the theory has...

the sense used in category theory, but not in the sense used by Hausmann and Ore. Nevertheless, influential books in semigroup theory, including Clifford...

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many expositions...

general is in category theory. The algebraic objects to which representation theory applies can be viewed as particular kinds of categories, and the representations...

morphisms. As such, it is a concrete category. The study of this category is known as group theory. There are two forgetful functors from Grp, M: Grp → Mon from...

that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine...

In category theory, a regular category is a category with finite limits and coequalizers of all pairs of morphisms called kernel pairs, satisfying certain...

In category theory, a branch of mathematics, a subobject is, roughly speaking, an object that sits inside another object in the same category. The notion...

3000 systems Image (category theory), a generalization of the image of a function Image (mathematics), subset of a function's codomain Image (matrix), or...

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal...