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Linear Bicategories: Quantales and Quantaloids

Banff International Research Station for Mathematical Innovation and Discovery

Linear bicategories were introduced by Cockett, Koslowski and Seely as the bicategorical version of linearly distributive categories. Such a bicategory B has two forms of composition related by a linear distribution. In this talk, we consider locally ordered linear bicategories of the form Q-Rel, i.e., relations valued in a quantale Q; as well as those B which are Girard bicategories. The latter provide examples which are not locally ordered; and they have the same relation to linear bicategories as â -autonomous categories have to linearly distributive categories. Examples include the bicategories Quant and Qtld, whose 1-cell are bimodules and objects are quantales and quantaloids, respectively. This is joint work with Rick Blute.

Mathematics; Category Theory; Homological Algebra; Algebraic Topology; Algebraic Structures

video/mp4

Author affiliation: Union College

2023-10-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86389

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/