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Description

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.