functor

== English == === Etymology === From function, modeled after factor. === Pronunciation === (Received Pronunciation) IPA(key): /ˈfʌŋktə/ === 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 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 {\displaystyle U} the operation of closure, regularization or relative completion, we obtain from a given functor F ∈ J F {\displaystyle {\mathcal {F}}\in {\mathcal {JF}}} the functors F ¯ : X → → F ( X → ) ¯ , F 0 : X → → F ( X → ) 0 , F c : X → → F ( X → ) c {\displaystyle {\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}} . 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 Σ ∗ {\displaystyle \Sigma _{*}} -objects and we review the relationship between Σ ∗ {\displaystyle \Sigma _{*}} -objects and functors. In short, a Σ ∗ {\displaystyle \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 → S ( M , X ) {\displaystyle S(M):X\rightarrow S(M,X)} , defined by a formula of the form S ( M , X ) = ⨁ r = 0 ∞ ( M ( r ) ⊗ X ⊗ r ) Σ r {\displaystyle 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 ==== ==== 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) === Further reading === “functor”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2026 == Romanian == === Etymology === Borrowed from French functeur. === Noun === functor m (plural functori) functor ==== Declension ==== == Spanish == === Noun === functor m (plural functores) alternative form of funtor