A fun example of a representable functor

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.

How do I think of a representable functor? - Math Stack Exchange

They aren't describing routes and locations per-se, but they are saying something that can be translated into routes and locations. These ...

Representable Functors: Practical Examples - Jobs

Representable Functors: Practical Examples · A functor f · An object a , such that f is the same as Hom a · A way to convert f into Hom a . That is ...

Interesting examples of functors : r/math - Reddit

A classical example is the endofunctor on finite dimensional vector spaces taking a vector space to its double dual.

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 ...

Are there examples where one proves something about the functor ...

So these are very naturally representable/co-representable properties. (A map X→Y is said to be a monomorphism if the maps ...

Representable Functors - The Unapologetic Mathematician

Now that we have a handle on hom functors, we can use them to define other functors. Since $latex \hom_\mathcal{C}$ is a functor from the ...

Fun With Representable Functors, or Why I Like Yondea's Lemma.

An object G \in \schmC together with morphisms m : G \times G \to G, i : G \to G and · We say that a group object (G, m, i, e) is commutative ...

Representable Functors - Bartosz Milewski's Programming Cafe

If F is a contravariant representable functor, then the representing type a = sqrt[x] {Fx}. ... 3. If F is an product type like A^x * B^x * … , ...

Representable Functors - C&C

In other words, Hom a takes an object b to the set of all morphisms a -> b . It takes an arrow b -> c to the function Hom a b -> Hom a c using ...

Category Theory II 4.1: Representable Functors - YouTube

Category Theory II 4.1: Representable Functors. 17K views · 7 ... Category Theory II 6.1: Examples of Adjunctions. Bartosz Milewski•9.8 ...

Representable functor - Wikipedia

In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets.

Optics and Representable Functors - Sonat Süer

To see these in action, we need representable functors. So here are two examples: Triple and WrappedStream . data Triple a ...

functor - What is Representable used for in Haskell? - Stack Overflow

And tabulate :: (Rep f -> a) -> f a constructs a container where each element is derived from its own index. Now, here is an example of a ...

nForum - representable functor - nLab

Mike: I disagree (partly). First of all, a functor F equipped with an isomorphism F ...

Radix Sort, Trie Trees, and Maps from Representable Functors

Representable Functors bring with them an intrinsic notion of sorting; not in the traditional 'ordered' sense, but rather a sense of 'structural' sorting.

Lecture 2: Moduli functors and Grassmannians

Definition 2. If F is representable by a scheme M, we say that M is a fine moduli space for the moduli problem F. Given a ...

Noob question about the type [Rep f] in the representable functor ...

it's called a representable functor, not a representable function. as in the category theory example? You didn't link nor quote that part. I ...

Representables and Yoneda 1 - YouTube

Definition of representable functors and the Yoneda embedding (though without calling it the Yoneda embedding yet)

Questions tagged [representable-functor] - Math Stack Exchange

Let C be a small category and let F∈Fun(Cop,Set) be a presheaf. I'm trying to show it is a colimit of representables using the fact that colimits in functor ...