Fuller's theorem on equivalences

On Monoidal Equivalences and Ann-equivalences

The equivalence between a monoidal category and a strict one has been proved by some authors such as Nguyen Duy Thuan [8], Christian Kassel [2], Peter Schauenburg [7]. In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M -functors and M morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic chara...

A dévissage theorem for modular exact categories with weak equivalences

In this note, we will introduce a notion of modularity of exact categories due to Masana Harada [Har05]. The naming is coming from the classical modular lattices theory [Bir48]. We will also state and prove so-called “homotopy Grayson-Staffeldt-Jordan-Hölder theorem” which is implicitly appeared in [Gra87] and [Sta89]. The theorem says contractibility of a simplicial set associated to a certain...

Equivalences on Petri nets

In this paper a set of Petri net equivalences is proposed. A correlation between all introduced equivalences is established, and a lattice of implications is obtained. In addition equivalences are examined on sequential nets. The process equivalences are demonstrated to be well discerning on this net class.

On Rickard's Equivalences

Equivalences on Observable Processes

The aim of this paper is to find the finest ‘observable’ and ‘implementable’ equivalence on concurrent processes. This is a part of a larger programme to develop a theory of observable processes where semantics of processes are based on locally and finitely observable process behaviour, and all process constructs are allowed, provided their operational meaning is defined by realistically implem...