The insidious bicategory of algebra bundles
Differential Geometry
2022-04-11 v1 Algebraic Topology
K-Theory and Homology
Abstract
In this paper we construct a bicategory of (super) algebra bundles over a smooth manifold, where the 1-morphisms are bundles of bimodules. The main point is that naive definitions of bimodule bundles will not lead to a well-defined composition law in such a bicategory, at least not if non-invertible bimodules and non-semisimple algebras are desired. This problem has not been addressed so far in the literature. We develop a complete solution, and also address symmetric monoidal structures as well as the corresponding questions of dualizability.
Keywords
Cite
@article{arxiv.2204.03900,
title = {The insidious bicategory of algebra bundles},
author = {Peter Kristel and Matthias Ludewig and Konrad Waldorf},
journal= {arXiv preprint arXiv:2204.03900},
year = {2022}
}
Comments
39 pages. Contains parts of arxiv:2106.12198v1, which we intent to split and will be modified