A peer-to-peer (p2p) system provides the networking substrate for the execution of distributed applications. It is made of peers that interact over an overlay network. Overlay networks are highly dynamic, as peers can join and leave at any time. Traditional process calculi, such as π-calculus, CCS and others, seem inadequate to capture these kinds of networks, their routing mechanisms, and to v...

due to difficulties in the application of traditional methods for identifying sediment sources, fingerprinting techniques, based on physical, chemical and organic properties of sediment and source materials, are increasingly being used as a valuable and effective alternative approach to obtain such information. the first step in this method is using an appropriate combination of diagnostic prop...

We have just seen that the category ∆ is equivalent to the subcategory consisting of the [n]. As a result, a simplicial set X• is given by specifying sets Xn for each n ∈ Z≥0, together with maps Xn → Xm for each map [m] → [n] in ∆. These maps are required to satisfy compatibility conditions (i.e., form a functor). The set Xn is called the set of n-simplices of X•. Example 1.3. Let X be a topolo...

We develop the theory of n-stacks (or more generally Segal n-stacks which are∞-stacks such that the morphisms are invertible above degree n). This is done by systematically using the theory of closed model categories (cmc). Our main results are: a definition of n-stacks in terms of limits, which should be perfectly general for stacks of any type of objects; several other characterizations of n-...

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In paper II, we studied the topos representations of the propositional language PL(S) for the case of qu...

The cubical sets model of Homotopy Type Theory introduced by Bezem, Coquand and Huber [2] uses a particular category of presheaves. We show that this presheaf category is equivalent to a category of sets equipped with an action of a monoid of name substitutions for which a finite support property holds. That category is in turn isomorphic to a category of nominal sets [15] equipped with operati...

1.1. Sites. We begin with the underlying idea for a Grothendieck topology. Consider your favorite topological space X. Its topology, don’t use the Zariski topology, is determined by the partially ordered category UX consisting of all the open subsets of X ordered with respect to inclusion. In order to verify that a presheaf is a sheaf on X, we must first construct all possible coverings U = (Ui...

In the present article we continue recent work in the direction of domain theory were certain (accessible) categories are used as generalized domains. We discuss the possibility of using certain presheaf toposes as generalizations of the Scott topology at this level. We show that the toposes associated with Scott complete categories are injective with respect to dense inclusions of toposes. We ...

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract defi...