There are infinitely many variants of the notion of Kan fibration that, together with suitable choices of cofibrations and the usual notion of weak equivalence of simplicial sets, ...
The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new hom...
We consider pseudo-descent in the context of 2-fibrations. A 2-category of descent data is associated to a 3-truncated simplicial object in the base 2-category. A morphism q in the...
Motivated by the question of the polytopal realizability of the simplicial complex n,k of (k + 1)-crossing-free sets of diagonals of the convex n-gon, we study the first open case...
We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...