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» Fibrations of Simplicial Sets
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ACS
2010
13 years 5 months ago
Fibrations of Simplicial Sets
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, ...
Tibor Beke
ACS
2004
13 years 4 months ago
Galois Theory and a New Homotopy Double Groupoid of a Map of Spaces
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...
Ronald Brown, George Janelidze
ACS
2004
13 years 4 months ago
Descent on 2-Fibrations and Strongly 2-Regular 2-Categories
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...
Claudio Hermida
CCCG
2009
13 years 2 months ago
On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon
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...
Jürgen Bokowski, Vincent Pilaud
DCG
2011
12 years 12 months ago
More Colourful Simplices
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 ...
Antoine Deza, Tamon Stephen, Feng Xie