Recent progress on defining abstract trace semantics for coalgebras rests upon two observations: (i) coalgebraic bisimulation for deterministic automata coincides with trace equivalence, and (ii) the classical powerset construction for automata determinization instantiates the generic idea of lifting a functor to the Eilenberg-Moore category of an appropriate monad T. We take this approach one ...

Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalised powe...

Abstract Let $\textsf{T}$ be a triangulated category with shift functor $\Sigma \colon \textsf{T} \to \textsf{T}$ . Suppose $(\textsf{A},\textsf{B})$ is co-t-structure coheart $\textsf{S} = \Sigma \textsf{A} \cap \textsf{B}$ and extended $\textsf{C} \Sigma^2 \textsf{B} \textsf{S}* \textsf{S}$ , which an extriangulated category. We show that there bijection between co-t-structures $(\textsf{A}^{...

Since the inception of the notion of fuzzy topology much attention was paid to the possible means of interaction between fuzzy and crisp topological settings, in order to see whether fuzzy topology was doing anything new. In particular, different functors relating the categories Top of topological spaces and L-Top of Ltopological spaces (L being a suitable complete lattice) appeared in the lite...

We describe the essential algebra, kBTˆ(G), of Burnside biset functor shifted by a group T, at G, in two cases. First, when G and T are both finite abelian groups k is field characteristic 0. In this case, kBTˆ(G) isomorphic to quotient star which defined terms subgroups G×G×T. The second case any satisfying (|G|,|T|)=1 commutative unitary ring. semidirect product Out(G) kBZ(G)(T), monomial rin...

In terms of category theory, the Gromov homotopy principle for a set valued functor F asserts that the functor F can be induced from a homotopy functor. Similarly, we say that the bordism principle for an abelian group valued functor F holds if the functor F can be induced from a (co)homology functor. We examine the bordism principle in the case of functors given by bordism groups of solutions ...

Applicative functors [6] are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell [5]. Applicative functors are to be preferred to monads when the structure of a computation is fixed a priori. That makes it possible to perform certain kinds of static analysis on applicative values. We define a notion of free applicative fu...