different between functor vs cofunctor
functor
English
Etymology
From function, modeled after factor.
Pronunciation
- (Received Pronunciation) IPA(key): /?f??kt?/
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
- 1991, Natalie Wadhwa (translator), Yu. A. Brudny?, 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
- (functional programming) A structure allowing a function to apply within a generic type, in a way conceptually similar to a functor in category theory.
Derived terms
- contravariant functor
- functor category
- representable functor
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–present.
Portuguese
Alternative forms
- funtor
Noun
functor m (plural functores)
- (category theory) functor (a mapping between categories)
functor From the web:
- what is functor in c++
- what are functor words
- what is functor in scala
- what is functor in prolog
- what is functor in haskell
- what is functor in java
- what does function mean
- what is functor in programming
cofunctor
English
Noun
cofunctor (plural cofunctors)
- A contravariant functor.
Further reading
- cofunctor on Wikipedia.Wikipedia
cofunctor From the web:
- what cofactor is required for acetyl-coa carboxylase activity
- what cofactors are needed for lipogenesis
- what cofactor is required for the transamination of serine
- what cofactor is required for transamination reactions
- what cofactor is required for the conversion of fumarate to succinate
- what cofactors and comorbidities are associated with anaphylaxis
- what cofactor is formed from vitamin b9
- what cofactors amplify anaphylaxis
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