### Definition of Functor

1. Noun. (grammar) a function word ¹

2. Noun. (computing) a function object ¹

3. Noun. (mathematics) 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'':''X''→''Y'' of ''C'' is mapped to a morphism ''F''(''f''): ''F''(''X'') → ''F''(''Y'') of ''D'', such that if $h = g \circ f$ then $F\left(h\right) = F\left(g\right) \circ F\left(f\right)$, and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant. ¹

¹ Source: wiktionary.com

### Functor Pictures

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### Lexicographical Neighbors of Functor

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### Literary usage of Functor

Below you will find example usage of this term as found in modern and/or classical literature:

1. Development of Mathematics in the 19th Century by Felix Klein, Robert Hermann (1979)
"THE CROSS-SECTION functor We have emphasized the "categorical" setting for the theory of ... We shall now define a "functor". vector bundles vector spaces ..."

2. Yang-Mills, Kaluza-Klein, and the Einstein Program by Robert Hermann (1978)
"THE CARTAN functor For each manifold X let M(X) — T(H) xR . ... L is called a Lagrangian for H. This correspondence L + 0(L) is the Cartan functor, ..."