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
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