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 then , 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, ..."
Other Resources Relating to: Functor
