Definitions for functor
ˈfʌŋk tərfunc·tor

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1. functor(Noun)

   a function word

2. functor(Noun)

   a function object

3. functor(Noun)

   a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:XY of C is mapped to a morphism F(f): F(X) F(Y) of D, such that if then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

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1. Functor

   A functor is a type of mapping between categories, which is applied in category theory. Functors can be thought of as homomorphisms between categories. In the category of small categories, functors can be thought of more generally as morphisms. Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are generally applicable in areas within mathematics that category theory can make an abstraction of. The word functor was borrowed by mathematicians from the philosopher Rudolf Carnap, who used the term in a linguistic context.

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Numerology

1. Chaldean Numerology

   The numerical value of functor in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of functor in Pythagorean Numerology is: 7

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