Related papers: On equivalences for cohomological Mackey functors

In equivariant algebra, Mackey functors replace abelian groups and incomplete Tambara functors replace commutative rings. In this context, we prove that equivariant Hochschild homology can sometimes be computed using Mackey functor-valued…

We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact $\Bbbk$-linear monoidal functor can be lifted…

Let $\mathcal{M}$ be an $n$-cluster tilting subcategory of ${\rm mod}\mbox{-}\Lambda$, where $\Lambda$ is an artin algebra. Let $\mathcal{S}(\mathcal{M})$ denotes the full subcategory of $\mathcal{S}(\Lambda)$, the submodule category of…

In the paper, we mainly connect the Gorenstein derived equivalence and stable functors of Gorenstein projective modules. Specially, we prove that a Gorenstein derived equivalence between CM-finite algebras A and B can induce a stable…

We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…

We prove that Hochschild cohomology of a certain class of fully group-graded algebras is a Mackey functor. We use the machinery of transfer maps between the Hochschild cohomology of symmetric algebras.

We show that the complete bornological convolution algebras of Lie groupoids and convolution bimodules of groupoid bibundles define a monoidal functor from the 2-category of differentiable stacks to the Morita 2-category of complete…

We prove that splendid Morita equivalences between principal blocks of finite groups with dihedral Sylow $2$-subgroups realised by Scott modules can be lifted to splendid Morita equivalences between principal blocks of finite groups with…

We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as…

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…

This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy types of their classifying spaces. Double categories (Ehresmann, 1963) have well-understood geometric realizations, and…

In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block $b$ and its Brauer correspondent and whose vertices have the same order as defect groups of the block $b$. The…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…

In this article we defined and studied quasi-finite comodules, the cohom functors for coalgebras over rings. linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing…

We point out that double categories provide a natural setting for modular functors obtained by a (bicategorical) string-net construction: The source of the modular functor -- which is now a double functor -- is a symmetric monoidal double…

In this paper, we show that stable functors of derived equivalences preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras. Then we generalize…

Given a p-block B of a finite group with defect group P and fusion system F on P we show that the rank of the group P/foc(F) is invariant under stable equivalences of Morita type. The main ingredients are the star-construction, due to Broue…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

We give a new formulation of Turing reducibility in terms of higher modalities, inspired by an embedding of the Turing degrees in the lattice of subtoposes of the effective topos discovered by Hyland. In this definition, higher modalities…