ENGLISH DICTIONARY

Functor

/ˈfʌŋktə/ · noun

Meaning

(grammar) A function word..

Definitions by Sense

(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.
(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.

Example Sentences

In the category of categories #92;mathbf#123;Cat#125; 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 U the operation of closure, regularization or relative completion, we obtain from a given functor ℱ∈𝒥ℱ the functors ◌̅F: overrightarrow X→◌̅F( overrightarrow X),F⁰: overrightarrow X→F( overrightarrow X)⁰,Fᶜ: overrightarrow X→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_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-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), defined by a formula of the form S(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ).

Given a homotopical category X and a functor u#58;A#92;rightarrowB, 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 Xᵘ#58;Xᴮ#92;rightarrowXᴬ (47.1).

Word Forms

functors

Related Words

When Should You Use Functor?

Use functor when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.

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Frequently Asked Questions

What does functor mean?

Functor means (grammar) A function word..

What is a synonym for functor?

The closest synonym depends on the sentence and intended sense.

What is the opposite of functor?

The opposite depends on the specific sense.

How do you use functor in a sentence?

In the category of categories #92;mathbf#123;Cat#125; the objects are categories and the morphisms are functors.

Sources & Attribution

FreeDictionaryAPI.com / Wiktionary · Original source · CC BY-SA 4.0

Dictionary data is provided by FreeDictionaryAPI.com and sourced from Wiktionary under its stated license.

ENGLISH DICTIONARY

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Definitions by Sense

(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.

(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.

Example Sentences

In the category of categories #92;mathbf#123;Cat#125; 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 U the operation of closure, regularization or relative completion, we obtain from a given functor ℱ∈𝒥ℱ the functors ◌̅F: overrightarrow X→◌̅F( overrightarrow X),F⁰: overrightarrow X→F( overrightarrow X)⁰,Fᶜ: overrightarrow X→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_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-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), defined by a formula of the form S(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ).

Given a homotopical category X and a functor u#58;A#92;rightarrowB, 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 Xᵘ#58;Xᴮ#92;rightarrowXᴬ (47.1).

Frequently Asked Questions

What does functor mean?

Functor means (grammar) A function word..

What is a synonym for functor?

The closest synonym depends on the sentence and intended sense.

What is the opposite of functor?

The opposite depends on the specific sense.

How do you use functor in a sentence?

In the category of categories #92;mathbf#123;Cat#125; the objects are categories and the morphisms are functors.

Sources & Attribution

FreeDictionaryAPI.com / Wiktionary · Original source · CC BY-SA 4.0

Dictionary data is provided by FreeDictionaryAPI.com and sourced from Wiktionary under its stated license.