A functor is defined which detects stable equivalences of symmetric spectra. As an application, the definition of topological Hochschild homology on symmetric ring spectra using the Hochschild complex is shown to agree with Bökstedt’s original ad hoc definition. In particular, this shows that Bökstedt’s definition is correct even for non-connective, non-convergent symmetric ring spectra. Mathem...

The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of -1-connective spectra. Introduction Since the early seventies it has been known that the classifying spaces of small symmetric monoidal categories are infinite loop spaces, the zeroth space in a spectrum...

Abstract We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain proof of the finite generation symmetric tensor categories in characteristic zero, as conjectured by Etingof and Ostrik. Moreover, such also determine representation dimension Rouquier stable category. Finally, recover number results on stably equivalent singula...

"Starting with group graded Morita equivalences, we obtain equivalences for tensor products and wreath products."

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing the reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric failure equivalences, which take two previously-known behavioral equivalences, i.e., the weak failure equivalence and the weak impossible future equivalence, as thei...

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natur...

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric readiness equivalences, which take two previously-known behavioral equivalences, i.e., the weak readiness equivalence and the weak possible future equivalence, as their ...

We introduce and study the notions of a PAC substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [8]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generaliz...

Let X be a finite CW-complex. Denote by Sph(X) the abelian group of stable fibre-homotopy classes of spherical fibrations on X. Let F (n) be the monoid of self-homotopy-equivalences of S and let F := colimn→∞ F (n). The classifying space BF represents Sph(X), i.e. Sph(X) ∼= [X;BF ]. For any vector bundle ξ on X, let J(ξ) ∈ Sph(X) be the stable fibre homotopy class of the spherical fibration ξ \...