functor

Etymology
From, modeled after.

Noun

 * 1)  A function word.
 * 2)  A function object.
 * 3)  A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.
 * 4) * 1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,
 * Choosing for $$U$$ the operation of closure, regularization or relative completion, we obtain from a given functor $$\mathcal{F}\in\mathcal{JF}$$ the functors
 * $$\overline{F} : \overrightarrow{X} \rightarrow \overline{F(\overrightarrow{X})}, F^0 : \overrightarrow{X}\rightarrow F(\overrightarrow{X})^0, F^c : \overrightarrow{X} \rightarrow F(\overrightarrow{X})^c$$.
 * 1) * 2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,
 * In this chapter, we recall the definition of the category of $$\Sigma_*$$-objects and we review the relationship between $$\Sigma_*$$-objects and functors. In short, a $$\Sigma_*$$-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor $$S(M) : X\rightarrow S(M,X)$$, defined by a formula of the form
 * $$S(M,X) = \bigoplus^\infty_{r=0} \left ( M(r)\otimes X^{\otimes r}\right )_{\Sigma_r}$$.
 * 1)  A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.
 * 1) * 2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,
 * In this chapter, we recall the definition of the category of $$\Sigma_*$$-objects and we review the relationship between $$\Sigma_*$$-objects and functors. In short, a $$\Sigma_*$$-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor $$S(M) : X\rightarrow S(M,X)$$, defined by a formula of the form
 * $$S(M,X) = \bigoplus^\infty_{r=0} \left ( M(r)\otimes X^{\otimes r}\right )_{\Sigma_r}$$.
 * 1)  A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

Translations

 * Finnish: funktio-olio
 * French:


 * Bashkir: функтор
 * Chinese:
 * Mandarin: 函子
 * Finnish: funktori
 * French:
 * German: Funktor
 * Hungarian: funktor
 * Icelandic: varpi
 * Irish: feidhmeoir
 * Italian: funtore
 * Japanese: 関手
 * Kazakh: функтор
 * Kyrgyz: функтор
 * Polish: funktor
 * Portuguese: functor, funtor
 * Russian:
 * Spanish: funtor
 * Swedish:

Noun

 * 1)   a mapping between categories

Etymology
.