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1. Functor: A mapping from one category into another that is compatible with the category structure. More precisely, a covariant functor from a category $ \mathfrak K $ into a category $ \mathfrak C $ or, simply, a functor from $ \mathfrak K $ into $ \mathfrak C $, is ... (Mathematics) [100%] 2023-12-30
2. Functor: The term functor has two distinct meanings. In category theory, a functor is a map between categories satisfying certain relations. [100%] 2023-03-12 [Mathematics] [Computer Science]...
3. Functor: In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated ... (Mapping between categories) [100%] 2023-09-27 [Functors]
4. Functor (functional programming): In functional programming, a functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values inside a generic type without changing the structure of the generic type. In Haskell this ... (Functional programming) [100%] 2024-06-08 [Functional programming] [Software design patterns]...
5. Functoid: A functoid is a tool for applying methods to data via a GUI drag 'n drop interface from within the BizTalk Mapping tool. In a typical BizTalk map, the data is copied from a source to a destination by dragging ... [87%] 2023-12-14 [Inter-process communication]
6. Functions (mathematics): This page is about mathematical functions. For functions in the context of computer programming, see functions. (Mathematics) [87%] 2024-01-03 [Pre-Calculus]
7. Factors: $ \newcommand{\be}{'"`UNIQ-MathJax1-QINU`"' } $ $ \newcommand{\bx}{\bf{x}} $ $ \newcommand{\btheta}{\bf{\theta}} $ University of Puerto Rico, Rio Piedras, San Juan, Puerto Rico. \mathbf{Keywords:}Bayes Factors, Evidence of Models, Intrinsic Bayes Factors, Intrinsic Priors, Posterior Model Probabiities Suppose that ... (Mathematics) [83%] 2023-12-19 [Statprob]
8. Funtoro: FUNTORO es una marca subsidiaria del grupo Micro-Star International (MSI) con sede en Taiwán y un proveedor global de soluciones de telemáticas y de infoentretenimiento para vehículos comerciales y establecimientos. También es productor de equipos originales para fabricantes como ... [83%] 2023-12-30
9. Adjoint functors: In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being ... (Relationship between two functors abstracting many common constructions) [82%] 2024-01-11 [Adjoint functors]
10. Smooth functor: In differential topology, a branch of mathematics, a smooth functor is a type of functor defined on finite-dimensional real vector spaces. Intuitively, a smooth functor is smooth in the sense that it sends smoothly parameterized families of vector spaces ... [70%] 2023-12-30 [Functors]
11. Forgetful functor: In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output. For an algebraic structure of ... [70%] 2023-12-30 [Functors]
12. Signalizer functor: In mathematics, a signalizer functor gives the intersections of a potential subgroup of a finite group with the centralizers of nontrivial elements of an abelian group. The signalizer functor theorem gives conditions under which a signalizer functor comes from a ... [70%] 2022-06-09 [Finite groups]
13. Final functor: In category theory, the notion of final functor (resp. initial functor) is a generalization of the notion of final object (resp. [70%] 2023-11-12 [Functors]
14. Tilting functor: When studying an algebra $A$, it is sometimes convenient to consider another algebra, given for instance by the endomorphism of an appropriate $A$-module, and functors between the two module categories. For instance, this is the basis of the Morita ... (Mathematics) [70%] 2023-10-22
15. Hom functor: In mathematics, specifically in category theory, hom-sets (i.e. sets of morphisms between objects) give rise to important functors to the category of sets. (Functor mapping hom objects to an underlying category) [70%] 2023-08-25 [Functors]
16. Representable functor: A covariant (or contravariant) functor $ F $ from some category $ \mathfrak R $ into the category of sets $ \mathfrak S $ (cf. Sets, category of) that is isomorphic to one of the functors $$ H ( A, -) : \mathfrak R \rightarrow \mathfrak S ,\ \ X \mapsto H ... (Mathematics) [70%] 2023-11-14
17. Zuckerman functor: In mathematics, a Zuckerman functor is used to construct representations of real reductive Lie groups from representations of Levi subgroups. They were introduced by Gregg Zuckerman (1978). [70%] 2023-09-30 [Representation theory] [Functors]...
18. Diagonal functor: In category theory, a branch of mathematics, the diagonal functor C → C × C {\displaystyle {\mathcal {C}}\rightarrow {\mathcal {C}}\times {\mathcal {C}}} is given by Δ ( a ) = ⟨ a , a ⟩ {\displaystyle \Delta (a)=\langle a,a\rangle } , which maps objects as well ... [70%] 2023-12-30 [Category theory]
19. Monoidal functor: In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor between two monoidal categories consists of a functor between the categories, along with two coherence maps—a natural transformation and ... (Concept in category theory) [70%] 2023-01-31 [Monoidal categories]
20. Homology functor: A functor on an Abelian category that defines a certain homological structure on it. A system $ H = {( H _ {i} ) } _ {i \in \mathbf Z } $ of covariant additive functors from an Abelian category $ {\mathcal A} $ into an Abelian category $ {\mathcal ... (Mathematics) [70%] 2023-10-19