functor

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 (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities. (C)

(hyper)

(hypo)

5. 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.

6. {{quote-book|en|year=2004|author=William G. Dwyer; Philip S. Hirschhorn; Daniel M. Kan; Jeffrey H. Smith|title=Homotopy Limit Functors on Model Categories and Homotopical Categories|publisher=American Mathematical Society|pageurl=https://books.google.com.au/books?id=km7zBwAAQBAJ&pg=PA165&dq=%22functor%22%7C%22functors%22&hl=en&sa=X&ved=0ahUKEwiB98r72dLaAhUIAXwKHaZHCd8Q6AEIhAEwEAv=onepage&q=%22functor%22%7C%22functors%22&f=false|page=165

7. 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}.

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

9. (l) (gloss)

10. (l)