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노트

위키데이터

• ID : Q386320

말뭉치

1. Let’s use this idea to guide us to finding some simple representable functors.
2. So we can actually build out applicatives from a representable functor.
3. convinced you that representable functors are interesting, remember, we were able to build all of this from a simple isomorphism with Hom .
4. Formally, there’s an isomorphism from any Representable Functor to Reader.
5. This package provides representable functors for haskell.
6. Today I want to discuss representable functors and Yondea's lemma which is, for example, used a lot in modern Algebraic Geometry.
7. We begin with the definition of a representable functor.
8. In a nutshell, this result says that representable functors are the same as group objects in , and that representable functors are the same as commutative group objects in .
9. The concept of a representable functor arose first in algebraic geometry (cf.
10. Representable functors occur in many branches of mathematics besides algebraic geometry.
11. The theorem (above) characterizing natural transformations from a representable functor to an arbitrary functor is commonly called the Yoneda lemma.
12. Representable functors are naturally isomorphic to Hom functors and therefore share their properties.
13. In particular, (covariant) representable functors preserve all limits.
14. Let’s analyze the definition of the representable functor from this perspective.
15. In the same vein we can think of representable functors as containers for storing memoized results of function calls (the members of hom-sets in Haskell are just functions).
16. Finally, notice that a representable functor gives us two different implementations of the same thing — one a function, one a data structure.
17. We will show that a functor that is a sheaf for the Zariski topology and has an open covering by representable functors is itself representable.
18. A query discussion on differences between representable functor and representation of a functor is archived here.

메타데이터

위키데이터

• ID : Q386320

Spacy 패턴 목록

• [{'LOWER': 'representable'}, {'LEMMA': 'functor'}]