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 ...

Among finite dimensional algebras over a field K, the class of gentle is known to be closed by derived equivalences. Although classification up equivalences usually difficult problem, Avella-Alaminos and Geiss have introduced invariants for A, which can calculated combinatorially from their bound quivers, applicable such classification. Ladkani has given formula describe dimensions Hochschild c...

Generalized Reynolds ideals are ideals of the center of a symmetric algebra over a field of positive characteristic. They have been shown by the second author to be invariant under derived equivalences. In this paper we determine the generalized Reynolds ideals of algebras of dihedral and semidihedral type (as defined by Erdmann), in characteristic 2. In this way we solve some open problems abo...

In this article we prove derived invariance of Hochschild-Mitchell homology and cohomology and we extend to k-linear categories a result by Barot and Lenzing concerning derived equivalences and one-point extensions. We also prove the existence of a long exact sequence à la Happel and we give a generalization of this result which provides an alternative approach. 2000 Mathematics Subject Classif...

This is a summary of a talk given at the Vienna homological mirror symmetry conference in June 2006. We review how both derived categories and stacks enter physics. In both cases, equivalences are realized via renormalization group flow: in the case of derived categories, (boundary) renormalization group flow realizes the mathematical procedure of localization on quasi-isomorphisms, and in the ...

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...