In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In par...

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.

Behavioural equivalences on open systems are usually defined by comparing system behaviour in all environments. Due to this “universal” quantification over the possible hosting environments, such equivalences are often difficult to check in a direct way. Here, working in the setting of process calculi, we introduce a hierarchy of behavioural equivalences for open systems, building on a previous...

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.