On the comparison of spans and bisets
Category Theory
2020-09-10 v2 Group Theory
Representation Theory
Abstract
We compare the bicategory of spans with that of bisets (a.k.a. bimodules, distributors, profunctors) in the context of finite groupoids. We construct in particular a well-behaved pseudo-functor from spans to bisets. This yields an application to the axiomatic representation theory of finite groups, namely a new proof and a strengthening of Ganter and Nakaoka's identification of Bouc's category of biset functors as a reflective subcategory of global Mackey functors. To this end, we also prove a tensor-monadicity result for linear functor categories.
Cite
@article{arxiv.2006.10375,
title = {On the comparison of spans and bisets},
author = {Ivo Dell'Ambrogio and James Huglo},
journal= {arXiv preprint arXiv:2006.10375},
year = {2020}
}
Comments
28 pages. Final version, to appear in Cah. Topol. G\'eom. Differ. Cat\'eg