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...

Cokernel Pushout (category theory) Direct limit Biproduct Direct sum Preadditive category Additive category Pre-Abelian category Abelian category Exact sequence...

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

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and colimits, like the strongly related notions...

relation Pullback (category theory) Pushout (category theory) Cobordism span at the nLab Yoneda, Nobuo (1954). "On the homology theory of modules". J. Fac...

In category theory, a branch of mathematics, the center (or Drinfeld center, after Soviet-American mathematician Vladimir Drinfeld) is a variant of the...

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...

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

In category theory, an end of a functor S : C o p × C → X {\displaystyle S:\mathbf {C} ^{\mathrm {op} }\times \mathbf {C} \to \mathbf {X} } is a universal...

object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that...

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...

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

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

the second equalizing. Remarks: Finite bicompleteness of the category ensures that pushouts and equalizers exist. ( I m , m ) {\displaystyle (Im,m)} can...

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...

symmetric polynomial, in commutative algebra Prefix sum, in computing Pushout (category theory) (also called an amalgamated sum or a cocartesian square, fibered...

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...

the category. They are also used in the definition of an enriched category. Monoidal categories have numerous applications outside of category theory proper...

In category theory and related fields of mathematics, an envelope is a construction that generalizes the operations of "exterior completion", like completion...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between 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...

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

measure induced on the target measure space by a measurable function Pushout (category theory), the categorical dual of pullback Direct image sheaf, the pushforward...

B\twoheadrightarrow A'} is a quotient map, i.e. a pushout of the first one along the zero map A → 0. This category has a natural Waldhausen structure, and the...

Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer...

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

disk), the two pushouts are not homotopy (or weakly) equivalent. Therefore, the pushout is not well-aligned with a principle of homotopy theory, which considers...

In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start...