functor in Czech

functor <n.> funktor Entry edited by: B2

Sentence patterns related to "functor"

1. The double dual functor is naturally isomorphic to the identity functor on LCA.

2. Define the functor S * as follows:

3. H-equivariant) deformation functor of X/H (resp.

4. It uses the exact functor theorem.

5. A category with a faithful functor to Set is (by definition) a concrete category; in general, that forgetful functor is not full.

6. Every representable functor C → Set preserves limits (but not necessarily colimits).

7. First, recall that an additive functor is a functor F: C → D between preadditive categories that acts as a group homomorphism on each hom-set.

8. Monad, Applicative functor, and functor are just functional programming patterns you can use to deal with effects like lists/arrays, trees, hashes/dictionaries, and even functions.

9. F is a functor, hence a presheaf, because it is constant.

10. At the cost of some repetition (compare adjoint functor), we outline how one gets from the hom-functor formulation of Adjunction in Cat to the elementary definition in terms of units and counits.

11. Note that Hk is a contravariant functor while Hn − k is covariant.

12. Σ gives rise to a functor from the category of pointed spaces to itself.

13. The reflector is the functor which sends each group to its abelianization.

14. (A functor is simply exact if it's both left exact and right exact.)

15. However, as a natural quantization scheme (a functor), Weyl's map is not satisfactory.

16. Applicatives Laws (2B) 3 Young Won Lim 3/6/18 The definition of Applicative class (Functor f) => Applicative f where pure:: a -> f a (<*>) :: f (a -> b) -> f a -> f b The class has a two methods : pure brings arbitrary values into the functor (<*>) takes a function wrapped in a functor f and a value wrapped in a functor f and returns the result of the application

17. A Maybe implements all three, so it is a functor, an Applicative, and a monad

18. A right adjoint to a forgetful functor is called a cofree functor; in general, right Adjoints may be thought of as being defined cofreely, consisting of anything that works in an inverse, regardless of whether it’s needed

19. For technical reasons, the category Ban1 of Banach spaces and linear contractions is often equipped not with the "obvious" forgetful functor but the functor U1 : Ban1 → Set which maps a Banach space to its (closed) unit ball.

20. This leads to the clarifying concept of natural transformation, a way to "map" one functor to another.

21. Note that an exact functor, because it preserves both kernels and cokernels, preserves all images and coimages.

22. One may also start with a contravariant left-exact functor F; the resulting right-derived functors are then also contravariant.

23. In this note, we introduce a criterion to detect vanishing of essential algebras of a Green Biset functor by means of morphisms

24. The fact that there does not exist any faithful functor from hTop to Set was first proven by Peter Freyd.

25. Now we can construct a functor from the category... from the category of Top 2 to the category of chain complexes.

26. To get back to actual topological spaces, there is a geometric realization functor which turns simplicial sets into compactly generated Hausdorff spaces.

27. The extension property makes β a functor from Top (the category of topological spaces) to CHaus (the category of compact Hausdorff spaces).

28. This leads to a variety of interesting other Adjunctions, including a chain of six (sometimes seven) adjoints involving the restriction functor to a

29. In the beginning of the 1970s, he proved his exact functor theorem, which allows the construction of a homology theory from a formal group law.

30. In this post, I will demonstrate the concepts related to Applicative functor via Java code examples and suggest areas where they are relevant/best suited

31. We introduce the inflation morphism and restriction morphism to prove that the essential supports of a Green Biset functor and its shifted functors are the same

32. It doesn't provide a default implementation for any of them, so we have to define them both if we want something to be an Applicative functor

33. Pretalk Adjunctions and monads Weighted limits Algebras and descent data Monadicity and descent Homotopy coherent Adjunctions A homotopy coherent adjunction in an (1;2)-category K is a simplicial functor Adj !K

34. Likewise, monoid homomorphisms are just functor s between single object categories. In this sense, category theory can be thought of as an extension of the concept of a monoid.

35. Our in tended readership is familiar with the notion of category, functor, and naturalit y, and either ab out to learn Adjunctions or in terested a calculational approac h to category theory

36. An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.

37. Then it turns out that a functor between pre-abelian categories is left exact if and only if it is additive and preserves all kernels, and it's right exact if and only if it's additive and preserves all cokernels.