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colimit functor

См. также в других словарях:

  • 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 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

  • Inverse image functor — In mathematics, the inverse image functor is a contravariant construction of sheaves. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle… …   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

  • 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

  • Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

  • Diagram (category theory) — 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 the categorical setting one has morphisms. An indexed family of sets is a collection of sets …   Wikipedia

  • Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… …   Wikipedia

  • Equivalence of categories — In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are essentially the same . There are numerous examples of categorical equivalences… …   Wikipedia

  • Initial and terminal objects — Terminal element redirects here. For the project management concept, see work breakdown structure. In category theory, an abstract branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C,… …   Wikipedia

  • Kan extension — Kan extensions are universal constructs in category theory, a branch of mathematics. They are closely related to adjoints, but are also related to limits and ends. They are named after Daniel M. Kan, who constructed certain (Kan) extensions using …   Wikipedia

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