`Double modules', double categories and groupoids, and a new homotopical double groupoid
Category Theory
2009-03-21 v2 Algebraic Topology
Abstract
We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting of a space, two subspaces, and a set of base points, under a condition which also implies that this double groupoid contains two second relative homotopy groups.
Keywords
Cite
@article{arxiv.0903.2627,
title = {`Double modules', double categories and groupoids, and a new homotopical double groupoid},
author = {Ronald Brown},
journal= {arXiv preprint arXiv:0903.2627},
year = {2009}
}
Comments
7 pages, 1 figure, QED.sty v.2 This version explains and proves the relation of the homotopy double groupoid with two second relative homotopy groups. Also extra references added