Double Loop Spaces, Braided Monoidal Categories and Algebraic 3-Type of Space (1997)
| Venue: | Math |
| Citations: | 17 - 2 self |
BibTeX
@INPROCEEDINGS{Berger97doubleloop,
author = {Clemens Berger},
title = {Double Loop Spaces, Braided Monoidal Categories and Algebraic 3-Type of Space},
booktitle = {Math},
year = {1997},
pages = {49--66}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We show that the nerve of a braided monoidal category carries a natural action of a simplicial E2-operad and is thus up to group completion a double loop space. Shifting up dimension twice associates to each braided monoidal category a 1-reduced lax 3-category whose nerve realizes an explicit double delooping whenever all cells are invertible. We deduce that lax 3-groupoids are algebraic models for homotopy 3-types. Introduction The concept of braiding as a refinement of symmetry is the starting point of a rich interplay between geometry (knot theory) and algebra (representation theory). The underlying structure of a braided monoidal category reveals an interest of its own in that it encompasses two at first sight different geometrical objects : double loop spaces and homotopy 3-types. The link to double loop spaces was pointed out by J. Stasheff [38] and made precise by Z. Fiedorowicz [15], who proves that double loop spaces may be characterized (up to group completion) as algebras o...
