functor
English
Etymology
From function, modeled after factor.
Pronunciation
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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.
- Hyponym: endofunctor
- In the category of categories, , the objects are categories and the morphisms are functors.
- 1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,
- Choosing for the operation of closure, regularization or relative completion, we obtain from a given functor the functors
- .
- Choosing for the operation of closure, regularization or relative completion, we obtain from a given functor the functors
- 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 and a functor , a homotopical -colimit (resp. -limit) functor on will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor (47.1).
- 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 -objects and we review the relationship between -objects and functors. In short, a -object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor , defined by a formula of the form
- .
- In this chapter, we recall the definition of the category of -objects and we review the relationship between -objects and functors. In short, a -object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor , defined by a formula of the form
Derived terms
Translations
grammar: function word — see function word
object-oriented programming: function object
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category theory: category mapping
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Further reading
- function word on Wikipedia.Wikipedia
- functor on Wikipedia.Wikipedia
- “functor”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.
Portuguese
Alternative forms
Noun
functor m (plural functores)
- (category theory) functor (a mapping between categories)
Categories:
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- English terms with IPA pronunciation
- English lemmas
- English nouns
- English countable nouns
- en:Grammar
- en:Object-oriented programming
- en:Category theory
- English terms with usage examples
- en:Algebra
- en:Logic
- Portuguese lemmas
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- Portuguese countable nouns
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- pt:Category theory