English

`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