Models of concurrent systems employ a wide variety of semantics inducing various notions of process equivalence, ranging from linear-time semantics such as trace equivalence to branching-time semantics such as strong bisimilarity. Many of these generalize to system types beyond standard transition systems, featuring, for example, weighted, probabilistic, or game-based transitions; this motivate...

If M is a model category and Z is an object of M, then there are model category structures on the categories (M ↓Z) (the category of objects of M over Z) and (Z ↓M) (the category of objects of M under Z) under which a map is a cofibration, fibration, or weak equivalence if and only if its image in M under the forgetful functor is, respectively, a cofibration, fibration, or weak equivalence. It ...

A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids. Basic properties of the Poisson K-ring are proved and the Poisson K-rings are calculated for a number of examples. In particular, for the zero Poisson structure ...

FuTS, state-to-function transition systems are generalizations of labeled transition systems and of familiar notions of quantitative semantical models as continuous-time Markov chains, interactive Markov chains, and Markov automata. A general scheme for the definition of a notion of strong bisimulation associated with a FuTS is proposed. It is shown that this notion of bisimulation for a FuTS c...

We want F to satisfy some kind of Mayer-Vietoris property, or excision. Hence, we assume C and D are proper, in that the pushout of a weak equivalence along a cofibration is also a weak equivalence. We’ll also ask that in D, sequential colimits of homotopy Cartesian cubes are again homotopy Cartesian, and we’ll elaborate on what this means. We also place a condition on F : Goodwillie calls it “...

Labeled state-to-function transition systems, FuTSs for short, capture transition schemes incorporating multiplicities from states to functions of finite support over general semirings. As such FuTSs constitute a convenient modeling instrument to deal with process languages and their stochastic extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed fr...

Every endofunctor B on the category Set can be lifted to a fibred functor on the category (fibred over Set) of equivalence relations and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback ...

Let G be a reductive group scheme over the p-adic integers, and let $$\mu $$ minuscule cocharacter for G. In Hodge-type case, we construct functor from nilpotent $$(G,\mu )$$ -displays p-nilpotent rings R to formal p-divisible groups equipped with crystalline Tate tensors. When R/pR has p-basis étale locally, show that this defines an equivalence between two categories. The definition of relies...