functor

Pronunciation Noun

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Pronunciation 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, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.*hypo*en*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*, Volume I, Elsevier (North-Holland), page 143 ↗,**Functors**and Interpolation Spaces- 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.

- Choosing for U the operation of closure, regularization or relative completion, we obtain from a given
**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).

- Given a homotopical category X and a
**2009**, Benoit Fresse,*Modules Over Operads and*, Springer, Lecture Notes in Mathematics: 1967, page 35 ↗,**Functors**- 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}.

- In this chapter, we recall the definition of the category of \Sigma_*-objects and we review the relationship between \Sigma_*-objects and

- French: foncteur

- French: foncteur
- German: Funktor
- Italian: funtore
- Portuguese: functor, funtor
- Russian: функтор
- Spanish: funtor

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003