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arXiv · 2204.03900

The insidious bicategory of algebra bundles

Peter Kristel·Matthias Ludewig·Konrad Waldorf
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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.

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Peter Kristel, Matthias Ludewig, Konrad Waldorf. 2022-04-08. The insidious bicategory of algebra bundles. https://arxiv.org/abs/2204.03900

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