Australian Category Seminar

Constructing linear bicategories from quantales and quantaloids

Rose Kudzman-Blaisยท27 November 2024

Linear bicategories, introduced by Cockett and Seely, model non-commutative multiplicative linear logic and serve as the bicategorical analogue of linearly distributive categories. A linear bicategory is characterized by two forms of composition, each defining a bicategory structure, with the two compositions interconnected through a linear distribution. In this talk, I will present joint work with co-authors Blute and Niefield, which focuses on developing examples of linear bicategories using quantales and quantaloids. It is well-known in monoidal topology that the category of quantale-valued relations forms a quantaloid, this framework extends to linear bicategories when the quantale itself is linearly distributive. Moreover, established constructions in the theory of categories enriched in a bicategory, within the context of quantaloids, can be adapted to construct linear bicategories. These extensions yield further novel examples and interesting closure results.

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