**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 $h\; =\; g\; \backslash circ\; f$ then $F(h)\; =\; F(g)\; \backslash circ\; F(f)$, 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*

### Definition of Functor

**1.** one that functions [n -S] - See also: functions

### Functor Pictures

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### Lexicographical Neighbors of Functor

### 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**, ..."