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John Baez (Mar 27 2020 at 00:02):This will be at 4-5 pm UTC, which is noon-1 pm Boston time. The talk is broadcast over YouTube here:
https://www.youtube.com/playlist?list=PLhgq-BqyZ7i6Vh4nxlyhKDAMhlv1oWl5n
with discussion here on Zulip.
Abstract. So-called "regular logic" is logic constrained to truth, conjunction, and existential quantification, forming the logical substrate of a form of relational calculus with equality. From a categorical perspective, following Carboni-Walters, such relational calculus may be captured by the notion of a "discrete cartesian bicategory", aka a "bicategory of relations", in which equality behaves according to rules familiar from the study of symmetric Frobenius monoids. The close connection between Frobenius monoids and 2-dimensional cobordisms suggests the possibility of developing "surface diagrams" (and certain "directed" cobordisms between them), akin to string diagrams but one dimension up, to represent the syntax, i.e., the structure of free discrete cartesian bicategories. This talk will outline some ideas and speculations on how I think this might work.