Functor

English

Etymology

From Template:M, modeled after Template:M.

Pronunciation

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Noun

1. Template:Lb A function word.
2. Template:Lb A function object.
3. Template:Lb 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. Template:C

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   • 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 $ℱ\in 𝒥ℱ$ the functors

     $\bar{F}:\overrightarrow{X}\to \overline{F(\overrightarrow{X})},F^0:\overrightarrow{X}\to F(\overrightarrow{X}{)}^0,F^c:\overrightarrow{X}\to F(\overrightarrow{X}{)}^c$.

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   • 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 ${\mathrm{\Sigma }}_{*}$-objects and we review the relationship between ${\mathrm{\Sigma }}_{*}$-objects and functors. In short, a ${\mathrm{\Sigma }}_{*}$-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor $S(M):X\to S(M,X)$, defined by a formula of the form

     $S(M,X)=\underset{r=0}{\overset{\mathrm{\infty }}{⨁}}{(M(r)\otimes X^{\otimes r})}_{{\mathrm{\Sigma }}_r}$.

4. Template:Lb A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

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Portuguese

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Noun

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Romanian

Etymology

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Noun

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