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Frobenius functor

WebOct 24, 2024 · We prove that if the Frobenius functor F (from the category of left R-modules to the category of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is equal ... WebFor example, basic properties of the Nakayama functor imply the categorical Radford S 4-formula for finite tensor categories [16], a Frobenius property of tensor functors between finite tensor categories [29], and a criterion for a finite tensor category to be symmetric Frobenius [17].

Introduction Frobenius functor

WebFrobenius' theorem (usual form) A smooth regular distribution is integrable iff it is involutive. Or in terms of vector fields: a set of r smooth vector fields, X 1 ,…, Xr, on a manifold M, … WebDec 15, 2024 · A typical example of Frobenius functor is the induction functor Ind H G = R G ⊗ R H − for group rings, where H ⊆ G is a subgroup with finite index. Faithful Frobenius functors arise naturally in stable equivalences of Morita type, and in singular equivalences of Morita type; see for examples [14], [30], [41], [43]. teak 24 https://ajliebel.com

Frobenius functors and Gorenstein flat dimensions

WebNov 15, 2024 · Frobenius pairs and Gorenstein projective objects. In this section, we prove that a faithful Frobenius functor preserves the Gorenstein projective dimension of … WebNov 15, 2024 · Section snippets Adjoint pairs and Frobenius pairs. In this section, we recall standard facts and examples on Frobenius functors. Throughout, we assume that both A and B are abelian categories with enough projective objects. Denote by P (A) and P (B) the full subcategories of projective objects in A and B, respectively.. Let F: A → B be an … WebA fully faithful functor Fis Frobenius if and only if it is part of an adjoint triple LaFaRwhere the canonical map σis a natural isomorphism. Proof. If Fis Frobenius, then there exists a functor Gsuch that (F,G) is a Frobenius pair. In particular, GaFaGis an ambidextrous adjunction. By taking L= G= R and by applying Proposition 1.2, we have ... teak 24 kleve

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Frobenius functor

Frobenius Equation -- from Wolfram MathWorld

WebJan 1, 2000 · frobenius functors and functor ca tegories φ from F un ( A − mod , B − mo d) to F un ( B , A ), where, if φ : F 1 → F 2 is a natural transformation between the functors … WebJun 9, 2024 · The main ingredient in the proof of Theorem 1.5 is the notion of a Frobenius functor which is an abstract version of the pullback functor under the Frobenius morphism from a group scheme to itself. The definition of this functor is given in Sect. 3 , and it works only in the case of semisimple pre-Tannakian categories.

Frobenius functor

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WebLet be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category , that extend the correspondi…

WebJan 1, 2000 · frobenius functors and functor ca tegories φ from F un ( A − mod , B − mo d) to F un ( B , A ), where, if φ : F 1 → F 2 is a natural transformation between the functors F 1 , F 2 : A − ... Webp-adically complete ring. In particular, forgetting the -structure de nes a functor from (R=A) to the category of p-adic enlargements of Spec(R). However, since we have forgetten the Frobenius lifts, the behaviour of coproducts (and thus also of cohomology) in (R=A) di ers from that in the category of p-adic enlargements of Spec(R).

WebDec 30, 2024 · This generalizes the usual Frobenius twist functor in modular representation theory and also one defined in arXiv:1503.01492, where it is used to show that if $\mathcal{C}$ is finite and ... WebThe exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long …

WebJun 27, 2007 · In particular, we introduce the notion of Frobenius homomorphism of coalgebras. The set of isomorphism classes of Frobenius functors between quite …

WebDec 15, 2024 · A typical example of Frobenius functor is the induction functor Ind H G = R G ⊗ R H − for group rings, where H ⊆ G is a subgroup with finite index. Faithful … ek god\u0027sWebMar 24, 2024 · The Frobenius equation is the Diophantine equation. where the are positive integers, is an integer, and the solutions are nonnegative integers. Solution of the … ek god god godWebJan 7, 2015 · 1 Answer. Let k be the field with p elements, A be the Hopf algebra k [ t] with Δ ( t) = t ⊗ 1 + 1 ⊗ t, and let F: A → A be its Frobenius map. If B is a k -algebra, then there is a bijection Φ: hom ( A, B) → B (with hom denoting algebra homomorphisms) given by Φ ( f) = f ( t). The comultiplication on A turns hom ( A, B) into a group ... teak 2x2WebMay 12, 2024 · Frobenius exact symmetric tensor categories. I will report on a joint work in progress with K. Coulembier and V. Ostrik. We show that a symmetric tensor category in characteristic p>0 admits a fiber functor to the Verlinde category (semisimplification of Rep (Z/p)) if and only if it has moderate growth and its Frobenius functor (an analog of ... teak 2x4WebAbstract. Given a complete, cocomplete category C, we investigate the problem of describing those small categories I such that the diagonal functor ∆ : C → Functors(I, C) is a Frobenius functor. This condition can be rephrased by saying that the limits and the colimits of functors I → C are naturally isomorphic. ek goddess\u0027sWebMar 1, 2024 · Since the completion functor ^: Sch k → fSch k {}^\hat\;:Sch_k\to fSch_k commutes with the above constructions the Frobenius morphism can be defined for formal k-schemes, too. In terms of symmetric products. We give here another characterization of the Frobenius morphism in terms of symmetric products. ek god\u0027s-pennyWebFrobenius ring homomorphism (i.e., f(r) = rpfor r2R). We let Rf denote the ring Rwith the R-Rbimodule structure given by rs:= rsand sr:= sf(r) for r2Rand s2Rf. Then F R( ) := Rf R is … ek godam ki bimari