# functor

suomi-englanti sanakirja

## functor englanniksi

1. A word.

2. A object.

3. 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. Category:en:Functions

4. (hypo)

5. 1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, ''Interpolation Functors and Interpolation Spaces'', Volume I, Elsevier (North-Holland), page 143,

6. 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.
7. 2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, ''Homotopy Limit Functors on Model Categories and Homotopical Categories'', (w), page 165,

8. 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).
9. 2009, Benoit Fresse, ''Modules Over Operads and Functors'', Springer, Lecture Notes in Mathematics: 1967, page 35,

10. 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}.
11. A structure allowing a function to apply within a type, in a way that is conceptually similar to a functor in category theory.

12. (l) (gloss)

13. (l)