set-valued functor

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• 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

• mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

• Subfunctor — In category theory, a branch of mathematics, a subfunctor is a special type of functor which is an analogue of a subset. Definition Let C be a category, and let F be a functor from C to the category Set of all sets. A functor G from C to Set is a …   Wikipedia

• Presheaf (category theory) — In category theory, a branch of mathematics, a V valued presheaf F on a category C is a functor F:C^mathrm{op} omathbf{V}. Often presheaf is defined to be a Set valued presheaf. If C is the poset of open sets in a topological space, interpreted… …   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

• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

• Pontryagin duality — In mathematics, in particular in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform. It places in a unified context a number of observations about functions on the… …   Wikipedia

• Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

• Element (category theory) — In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows to restate definitions or properties of morphisms (such as… …   Wikipedia

• Gelfand representation — In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings:* a way of representing commutative Banach algebras as algebras of continuous functions; * the fact that for commutative C*… …   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