We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck) toposes to locally presentable categories and from monomorphism to more general cofibrations. As in the original case, under additional conditions, the resulting model structures are ”left determined” in the sense of Rosický and Tholen.

Wreath products such as Z ≀ Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z ≀ Z as a subgroup of Thompson’s group F and as a subgroup of Baumslag’s metabelian group G. We find that Z ≀ Z is undistorted in F but is at least exponentially distorted in G.

Several methods for constructing left determined model structures are expounded. The starting point is Olschok’s work on locally presentable categories. We give sufficient conditions to obtain left determined model structures on a full reflective subcategory, on a full coreflective subcategory and on a comma category. An application is given by constructing a left determined model structure on ...

Quadratic Convex Reformulation (QCR) is a technique that was originally proposed for quadratic 0-1 programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible. In this paper, we focus on the case of quadratically...

It is argued that the ‘problem of time’ in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a (4 + 2n)-dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck tim...

We consider the problem of optimal decentralized controller synthesis. There are several classes of such problems for which effective solution methods are known, including the quadratically invariant one. In this paper, we use Gröbner bases and elimination theory to characterize all closed-loop maps achievable by forming a feedback loop with decentralized controllers. We show that this approach...

The theory of enriched accessible categories over a suitable base category V is developed. It is proved that these enriched accessible categories coincide with the categories of flat functors, but also with the categories of models of enriched sketches. A particular attention is devoted to enriched locally presentable categories and enriched functors.

A finitely presentable group G is hyperbolic if and only if the map H2 b (G, V ) → H2(G, V ) is surjective for any bounded G-module. The ‘only if’ direction is known and here we prove the ‘if’ direction. We also consider several ways to define a linear homological isoperimetric inequality.