What is functor?

Functor

In category theory, a branch of mathematics, a functor is a special type of mapping between categories. Functors can be thought of as homomorphisms between categories, or morphisms when in the category of small categories.

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Some articles on functor:

Amnestic Functor
... In the mathematical field of category theory, an amnestic functor F A → B is a functor for which A-isomorphism ƒ is an identity whenever Fƒ is an identity ...
Functor - Relation To Other Categorical Concepts
... The collection of all functors C→D form the objects of a category the functor category ... Morphisms in this category are natural transformations between functors ... Functors are often defined by universal properties examples are the tensor product, the direct sum and direct product of groups or vector spaces, construction of ...
Stone Functor
... In mathematics, the Stone functor is a functor S Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms ...
Size Functor
... real continuous function defined on it, the -th size functor, with, denoted by, is the functor in, where is the category of ordered real numbers, and is the category of ... to , for each, In other words, the size functor studies the process of the birth and death of homology classes as the lower level set changes ... When is smooth and compact and is a Morse function, the functor can be described by oriented trees, called − trees ...
Schur Functor
... field of representation theory, a Schur functor is a functor from the category of modules over a fixed commutative ring to itself ... Schur functors are indexed by partitions and are described as follows ... of R-modules is the image of E under the Schur functor indexed by λ ...