Representable functor
Representable functor - Wikipedia
Representable functor ... In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category ...
Representability is one of the most fundamental concepts of category theory, with close ties to the notion of adjoint functor and to the Yoneda lemma.
How do I think of a representable functor? - Math Stack Exchange
For any category C , a (covariant or contravariant) functor F:C→S e t is said to be representable if there is an object c in C so that for all ...
Representable Functors - Bartosz Milewski's Programming Cafe
a representable functor gives us two different implementations of the same thing — one a function, one a data structure. They have exactly the ...
A fun example of a representable functor | Lovely little lemmas
Let F \colon \mathscr C \to \Set be a functor. Then F is representable if it is isomorphic to \Hom(A,-) for some A \in \ob \mathscr C.
Category Theory For Beginners: Representable Functors - YouTube
We use the running example of the natural number object as the universal dynamical system to illustrate how representable functors can be ...
Category Theory II 4.1: Representable Functors - YouTube
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When does a "representable functor" into a category other than Set ...
If C is an ordinary category, then for any c∈C the covariant representable functor Hom(c,−):C→Set preserves limits.
representable functor theorem in nLab
As representable functors are closely connected to adjoint functors, this theorem is essentially equivalent to the adjoint functor theorem and to theorems ...
Data.Functor.Representable - Hackage
A Functor f is Representable if tabulate and index witness an isomorphism to (->) x. tabulate . index = id index . tabulate = id tabulate . return f = return f
how to prove that a non-representable functor is not representable
Sorry if this upsets you. It would be a crime to say anything about representable functors without men- tioning the Yoneda Lemma: Theorem 1 (Yoneda Lemma) ...
Representable Functors: Practical Examples - Jobs
A functor f is representable, if (1) it has a RepresentingObj f which represents it, and (2) there are functions to convert fx into (RepresentingObj f -> x).
A functor F:Cop→Setsκ (from a locally κ-small category) is said to be representable when it is naturally isomorphic to Hom(−,X) for an object X:C (called the ...
Representables and Yoneda 1 - YouTube
Definition of representable functors and the Yoneda embedding (though without calling it the Yoneda embedding yet)
lecture 13: representable functors and the brown
Representable functors. Let C be a category. A functor F : Cop → Sets is called representable if there exists an object.
Laziness with Representable Functors | by Brian Lonsdorf - Medium
We can convert any indexable data structure into its function form to achieve laziness. Formally, there's an isomorphism from any ...
Representable functor - Encyclopedia of Mathematics
A functor F:R→S is representable if and only if there is an object A∈ObR and an element a∈F(A) such that for every element x∈F(X), X∈ObR, there ...
Yoneda's lemma 1 2. Representable functors 2 2.
A functor h is representable (in the category of schemes) if there is a scheme X and an isomorphism of functors h → hX. Examples of representable functors. You ...
Representable Functor - (Category Theory) - Fiveable
A representable functor is a type of functor that is naturally isomorphic to the hom-functor, meaning it can be expressed as the set of morphisms from a fixed ...
Representable functors turn out to be extremely useful, as we'll see. As an example, consider the “underlying set” functor U:\mathbf{Grp}\rightarrow\mathbf{Set ...