Related papers: Morita equivalences between algebraic dependent ty…

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

We classify the rational Cherednik algebras H_c(W) (and their spherical subalgebras) up to isomorphism and Morita equivalence in case when W is the symmetric group and `c' is a generic parameter value.

We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.

We show that singular equivalences of Morita type with level between finite-dimensional Gorenstein algebras over a field preserve the (Fg) condition.

We present the rudiments of the Morita theory of module systems (over semirings), paralleling the classical Morita theory over associative rings.

Let $A$ and $B$ be two Morita equivalent finite dimensional associative algebras over a field $\Bbbk$. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with…

We consider how Morita equivalences are compatible with the notion of a corner subring. Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence…

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…

A meteor graph is a connected graph with no sources and sinks consisting of two disjoint cycles and the paths connecting these cycles. We prove that two meteor graphs are shift equivalent if and only if they are strongly shift equivalent,…

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 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…

We demonstrate that, in certain cases, quantization and the classical limit provide functors that are "almost inverse" to each other. These functors map between categories of algebraic structures for classical and quantum physics,…

Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd characteristic. This assumption on the characteristic is for…

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…

This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A layered theory is developed in the context of categories,…

We define a homotopy relation between arrows of a category with weak equivalences, and give a condition under which the quotient by the homotopy relation yields the homotopy category. In the case of the fibrant-cofibrant objects of a model…