Related papers: On iterated almost $\nu$-stable derived equivalenc…
In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. In particular, give a new proof of Caldararu's conjecture about Morita equivalences of Azumaya algebras on…
Invariants with respect to recollements of the stable category of Gorenstein projective A-modules over an algebra A and stable equivalences are investigated. Specifically, the Gorenstein rigidity dimension is introduced. It is shown that…
We survey the main results in Jeremy Rickard's seminal papers `Morita theory for derived categories' and `Derived equivalences and derived functors'. These papers catalysed the later development of the Morita theory of (enhanced) compactly…
Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…
From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…
We consider a variant of the notion of Morita equivalence appropriate to weak* closed algebras of Hilbert space operators, which we call {\em weak Morita equivalence}. We obtain new variants, appropriate to the dual algebra setting, of the…
Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dimensional algebras over fields by centralizers of matrices.…
Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an…
In his paper [Ric89], Rickard presents the stable module category of a self-injective algebra as a Verdier quotient of its derived category by perfect complexes. We present a similar realization of the homotopy category in hopfological…
Let $A$ be an Artin algebra and $F$ a non-zero subfunctor of $\Ext_A^{1}(-,-)$. In this paper, we characterize the relative $\phi$-dimension of $A$ by the bi-functor $\Ext_F^1(-,-)$. Furthermore, we show that the finiteness of relative…
Buan-Iyama-Reiten-Smith proved, based on Derksen-Weyman-Zelevinsky work, that the Jacobian algebra of two quivers with potential related by a QP-mutation are nearly Morita equivalent. They proved, using Axiom of Choice, that the natural…
It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.
We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras in [{\sc D. Vossieck}, {\em The algebras with discrete derived category}, J. Algebra {\bf…
In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…
Categorical equivalences between block algebras of finite groups - such as Morita and derived equivalences - are well-known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for…
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…
We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group $G$ is strongly-graded-equivalent to the skew group algebra by a product partial action of $G$. As to a…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of…
Let $(W,H,\mu)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity where the perturbation $u$ is an equivalence class w.r.to the Wiener measure. We study several necessary and sufficient conditions…