functor of inverse limit

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• Inverse limit — In mathematics, the inverse limit (also called the projective limit) is a construction which allows one to glue together several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse… …   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

• Inverse system — In mathematics, an inverse system in a category C is a functor from a small cofiltered category I to C . An inverse system is sometimes called a pro object in C .The category of inverse systemsPro objects in C form a category pro C . Two inverse… …   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

• 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

• Direct limit — In mathematics, a direct limit (also called inductive limit) is a colimit of a directed family of objects . We will first give the definition for algebraic structures like groups and modules, and then the general definition which can be used in… …   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

• Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… …   Wikipedia

• Initial topology — In general topology and related areas of mathematics, the initial topology (projective topology or weak topology) on a set X, with respect to a family of functions on X, is the coarsest topology on X which makes those functions continuous.The… …   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

• Formal group — In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were first defined in 1946 by S. Bochner. The term formal group sometimes means the same as formal group law,… …   Wikipedia