Related papers: Morita Equivalence
We show that several Morita equivalence classes of tame algebras do not occur as blocks of finite groups. This refines classifications by Erdmann of classes of blocks with dihedral, semidihedral, and generalised quaternion defect groups. In…
Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is…
We introduce Morita equivalence to the study of Kleene algebras and modules. Classical characterizations of Morita-equivalent semirings such as having equivalent categories of modules and one semiring being a full matrix algebra over the…
We develop a group graded Morita theory over a G-graded G-acted algebra, where G is a finite group.
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational…
We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…
Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
A finite pre-tensor category is a finite abelian category equipped with a right exact tensor product for which every projective object has duals. Finite tensor categories, for which every object has duals, are notable examples. More…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.
This note uses a variation of graded Morita theory for finite dimensional superalgebras to determine explicitly the graded basic superalgebras for all real and complex Clifford superalgebras. As an application, the Grothendieck groups of…
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond…
We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0)…
Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude…
I give a characterization of the conditions for two Hamiltonians to be equivalent, discuss the construction of the operators that relate equivalent Hamiltonians, and introduce variational methods that can select Hamiltonians with desirable…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…