diagonal functor
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Diagonal functor — In category theory, for any object a in any category where the product exists, there exists the diagonal morphism satisfying for , where πk … Wikipedia
Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… … Wikipedia
Diagonal — For the avenue in Barcelona, see Avinguda Diagonal. The diagonals of a cube with side length 1. AC (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length … Wikipedia
Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… … Wikipedia
Universal property — In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. These properties are called universal properties … Wikipedia
List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… … Wikipedia
Final topology — In general topology and related areas of mathematics, the final topology (inductive topology or strong topology) on a set X, with respect to a family of functions into X, is the finest topology on X which makes those functions continuous.… … Wikipedia
Cone (category theory) — In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances in category theory as well. Contents 1 Definition 2 Equivalent formulations 3 Category … Wikipedia
Coproduct — This article is about coproducts in categories. For coproduct in the sense of comultiplication, see Coalgebra. In category theory, the coproduct, or categorical sum, is the category theoretic construction which includes the disjoint union of sets … Wikipedia
