Pronunciations
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/ˈfʌŋktə/
Pronunciation notes
- Received-Pronunciation
Noun
A function word.
A function object.
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.
- Broader terms
- Examples
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In the category of categories #92;mathbf#123;Cat#125; the objects are categories and the morphisms are functors.
More examples (3)
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.
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).
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).
A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.