The main theorem of [4] say that there is a proper closed simplicial model category structure on the category Spt of symmetric spectra, and that the associated homotopy category Ho(Spt) is equivalent to the stable category. This paper shows how to generalize this result to the category PreSpt(C) of presheaves of symmetric spectra on an arbitrary small Grothendieck site C. The reader will observ...

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...

We check that there exists a model structure on the category of flows whose weak equivalences are the S-homotopy equivalences. As an application, we prove that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. The method of proof is completely different from the one of the third part of this series of papers.

The asymptotic normality of the sample mean of iid rv 's is equivalent to the well known conditions of Levy or Feller. More recently, additional equivalences have been developed in terms of the quantile function (qf). And other useful probabilistic equivalences could be cited. The emphasis here is on equivalences, and many other useful and informative equivalences will be developed. Many depend...

Consider two synchronously communicating systems p and q over finite agents. Assume that one wants to check whether p ,~ q for one of the commonly used equivalences. We show that this question is PSPACE hard for all equivalences which lie between strong bisimulation and trace equivalences. For some equivalences exponential lower and upper bounds are proven. We also show that this problem is NP ...

We give an overview of the computational complexity of all the equivalences in van Glabbeek's linear/branching time hierarchy and the preorders in the corresponding hierarchy of preorders. We consider nite state or regular processes as well as innnite-state BPA and BPP processes. A distinction, which turns out to be important in the nite-state processes, is that of simulation-like equivalences/...

We examine the problem of finite-state representability of infinitestate processes w.r.t. certain behavioural equivalences. We show that the classical notion of regularity becomes insufficient in case of all equivalences of van Glabbeek’s hierarchy except bisimilarity, and we design and justify a generalization in the form of strong regularity and finite characterizations. We show that the cond...

In this paper the process for turning a dependency-based corpus to a constituentbased one is explained. For this purpose, first both the Dependency and the Constituent formalism are analized and then the corresponding equivalences of linguistic phenomena are treated. This process has had different phases in which the linguistic equivalences have been improved. Finally, the evaluation process is...

The question that serves as the title is to be understood in the context of Quillen model categories: having fixed the category of models and the subcategory of weak equivalences, how much ambiguity is there in finding suitable fibration and cofibration classes? Already for simplicial sets, infinitely many different subclasses of the monomorphisms can serve as cofibrations (with the usual weak ...