We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasicoherent modules on schemes, in the differential-graded context, in stable homotopy theory as well as in the equivariant, motivic, and parametrized variant thereof. As an application of ...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

In the paper “Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities” to appear in Theoretical Computer Science, we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes. In particular, we consider strong trace, failure, testing, and bisimulation equivalences. For each of these groups of equivalences, we examine the...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular...

In this paper we propose a hierarchy of games that allows us to make a systematic comparison of process equivalences by characterizing process equivalences as games. The well-known linear/branching time hierarchy of process equivalences can be embedded into the game hierarchy, which not only provides us with a refined analysis of process equivalences, but also offers a guidance to defining inte...

This paper is concerned with the construction and analysis of multilevel Schwarz preconditioners for partition of unity methods applied to elliptic problems. We show under which conditions on a given multilevel partition of unity hierarchy (MPUM) one even obtains uniformly bounded condition numbers and how to realize such requirements. The main anlytical tools are certain norm equivalences base...

In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In par...