since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

A given monoid usually admits many presentations by generators and relations the notion of Tietze equivalence characterizes when two describe same monoid: it is case one can transform presentation into other using families so-called transformations. The goal this article to provide an abstract geometrical understanding well-known fact, constructing a model structure on category presentations, i...

"Starting with group graded Morita equivalences, we obtain equivalences for tensor products and wreath products."

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing the reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric failure equivalences, which take two previously-known behavioral equivalences, i.e., the weak failure equivalence and the weak impossible future equivalence, as thei...

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric readiness equivalences, which take two previously-known behavioral equivalences, i.e., the weak readiness equivalence and the weak possible future equivalence, as their ...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

In the paper “Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities” to appear in Theoretical Computer Science, we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes. In particular, we consider strong trace, failure, testing, and bisimulation equivalences. For each of these groups of equivalences, we examine the...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular...

In this paper we propose a hierarchy of games that allows us to make a systematic comparison of process equivalences by characterizing process equivalences as games. The well-known linear/branching time hierarchy of process equivalences can be embedded into the game hierarchy, which not only provides us with a refined analysis of process equivalences, but also offers a guidance to defining inte...