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.
- Pub Date:
- April 2022
- Mathematics - Differential Geometry;
- Mathematics - Algebraic Topology;
- Mathematics - K-Theory and Homology
- 39 pages. Contains parts of arxiv:2106.12198v1, which we intent to split and will be modified