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...

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

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

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, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

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...

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

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...

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...

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...

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...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

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

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...

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...

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...

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

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...

mathematics, an n-group, or n-dimensional higher group, is a special kind of n-category that generalises the concept of group to higher-dimensional algebra. Here...

In category theory and related fields of mathematics, a refinement is a construction that generalizes the operations of "interior enrichment", like bornologification...

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

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

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

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 Kleisli category is a category naturally associated to any monad T. It is equivalent to the category of free T-algebras. The Kleisli...

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

an exact category and the inclusion I is an exact functor. This occurs if and only if C is closed under pullbacks of epimorphisms and pushouts of monomorphisms...

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