2-Vector Spaces and Groupoids
Quantum Algebra
2010-03-30 v2 Category Theory
Abstract
This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between groupoids in both a covariant and contravariant way, which are ambidextrous adjoints. This is used to construct a representation--a weak functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail.
Cite
@article{arxiv.0810.2361,
title = {2-Vector Spaces and Groupoids},
author = {Jeffrey C. Morton},
journal= {arXiv preprint arXiv:0810.2361},
year = {2010}
}
Comments
44 pages, 5 figures - v2 adds new theorem, significant changes to proofs, new section