mathematics, a smooth functor is a type of functor defined on finite-dimensional real vector spaces. Intuitively, a smooth functor is smooth in the sense...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

series of a smooth function, hence the term "calculus of functors". Many objects of central interest in algebraic topology can be seen as functors, which are...

direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in...

the manifold itself. The structure sheaf of M, denoted Ck, is a sort of functor that defines, for each open set U ⊂ M, an algebra Ck(U) of continuous functions...

bundles in a functorial manner. This is made precise in the language of smooth functors. An operation of a different nature is the pullback bundle construction...

natural in the technical sense: if  f : M → N is a smooth map and Ωk is the contravariant smooth functor that assigns to each manifold the space of k-forms...

geometry, the exceptional inverse image functor is the fourth and most sophisticated in a series of image functors for sheaves. It is needed to express Verdier...

representation canonical bifunctor; but as (single) functor, of type [X, -], it appears as an adjoint functor to a functor of type (-×X) on objects; In functional...

called the tangent map. In this way, T {\displaystyle T} is a functor. Given a smooth map φ : M → N and a vector field X on M, it is not usually possible...