functor Hom

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• Hom functor — In mathematics, specifically in category theory, Hom sets, i.e. sets of morphisms between objects, give rise to important functors to the category of sets. These functors are called Hom functors and have numerous applications in category theory… …   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

• Functor category — In category theory, a branch of mathematics, the functors between two given categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. Functor categories are of… …   Wikipedia

• Representable functor — In mathematics, especially in category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i …   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

• Ext functor — In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic topology, but are common in many areas of mathematics. Definition and computation Let R be a ring and let mathrm{Mod}… …   Wikipedia

• Exact functor — In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations of… …   Wikipedia

• Forgetful functor — In mathematics, in the area of category theory, a forgetful functor is a type of functor. The nomenclature is suggestive of such a functor s behaviour: given some object with structure as input, some or all of the object s structure or properties …   Wikipedia

• Direct image functor — In mathematics, in the field of sheaf theory and especially in algebraic geometry, the direct image functor generalizes the notion of a section of a sheaf to the relative case. Contents 1 Definition 1.1 Example 1.2 Variants …   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