# functor
## English
### Etymology

From function, modeled after factor.

### Pronunciation

* (Received Pronunciation) IPA: /ˈfʌŋktə/
* Audio (US):(file)

### Noun

functor (plural functors)
* (grammar) A function word.
* (object-oriented programming) A function object.
* (category theory) 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.
    Hypernym: morphism
    Hyponym: endofunctor
    In the category of categories, $\mathbb {CAT}$, the objects are categories and the morphisms are functors.
** 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
       ${\overline {F}}:{\overrightarrow {X}}\rightarrow {\overline {F({\overrightarrow {X}})}},F^{0}:{\overrightarrow {X}}\rightarrow F({\overrightarrow {X}})^{0},F^{c}:{\overrightarrow {X}}\rightarrow F({\overrightarrow {X}})^{c}$.
** 2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165:Given a homotopical category $X$ and a functor $u:A\rightarrow B$, a homotopical $u$-colimit (resp. $u$-limit) functor on $X$ will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor $X^{u}:X^{B}\rightarrow X^{A}$ (47.1).
** 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
       $S(M,X)=\bigoplus _{r=0}^{\infty }\left(M(r)\otimes X^{\otimes r}\right)_{\Sigma _{r}}$.
* (functional programming) A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

#### Derived terms

* adjoint functor
* anafunctor
* bifunctor
* contravariant functor
* faithful functor
* forgetful functor
* full functor
* functor category
* functorial
* group functor
* identity functor
* overfunctor
* profunctor
* pseudofunctor
* representable functor
* subfunctor
* underlying functor
* Yoneda functor

#### Translations
### Further reading

* function word on Wikipedia.Wikipedia
* functor on Wikipedia.Wikipedia
* functor (functional programming) on Wikipedia.Wikipedia
* “functor”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.

## Portuguese
### Alternative forms

* funtor

### Noun

functor m (plural functores)
* (category theory) functor (a mapping between categories)

## Romanian
### Etymology

Borrowed from French functeur.

### Noun

functor m (plural functori)
* functor