Related papers: Some remarks on higher Morita categories
We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita…
As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita…
Our aim in this paper is to prove two results related to the three constructions of cluster categories: as orbit categories, as singularity categories and as cosingularity categories. In the first part of the paper, we prove the universal…
In this paper we study multiplicative structures on comodules over bialgebras in the setting of $\infty$-categories. We show that the $\infty$-category of comodules over an $(\mathcal{O},\mathbf{Ass})$-bialgebra in a mixed…
We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a…
We show that the Morse complex of a compact Lie monoid can be given the structure of an $f$-bialgebra, a chain-level version of bialgebras introduced in [CHM24]; and that this assignment defines an $\infty$-functor. As a consequence, we…
Coisotropic reduction from Poisson geometry and deformation quantization is cast into a general and unifying algebraic framework: we introduce the notion of coisotropic triples of algebras for which a reduction can be defined. This allows…
Let $T=(A,M,0,B)$ be a triangular matrix algebra with its corner algebras $A$ and $B$ Artinian and $_AM_B$ an $A$-$B$-bimodule. The 2-recollement structures for singularity categories and Gorenstein defect categories over $T$ are studied.…
In this article, we prove that, under certain conditions, Morita context algebras that arise from Igusa-Todorov (LIT) algebras and have zero bimodule morphisms are also Igusa-Todorov (LIT). For a finite dimensional algebra $A$, we prove…
This work is an attempt towards a Morita theory for stable equivalences between self-injective algebras. More precisely, given two self-injective algebras A and B and an equivalence between their stable categories, consider the set S of…
We introduce the notion of bi-monoid in general monoidal category generalizing by this the notion of bialgebra. In the case of bimodules over a noncommutative algebra, we obtain a compatibility condition between ring and coring whenever…
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules…
We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.
We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such…
We shall introduce the notions of the strong Morita equivalence for unital inclusions of unital $C^*$-algebras and conditional expectations from an equivalence bimodule onto its closed subspace with respect to conditional expectations from…
In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…
This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically…
The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We…
We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories and we use this to prove many classical results about monads in the $\infty$-categorical framework. Amongst other…
We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups…