July 10, 2020

Friday, July 17th, 2020, 11:00, on Zoom.

Jacopo Emmenegger (Birmingham)
Elementary doctrines as coalgebras (j.w.w. Fabio Pasquali and Pino Rosolini)


Lawvere’s hyperdoctrines mark the beginning of applications of category theory to logic. The connection between (typed) logical theories and certain functors taking values in the category of posets is exemplified by two embeddings: of elementary doctrines into primary ones, and of elementary doctrines with effective quotients into elementary ones. In logical terms these correspond to the inclusion of Λ=-theories into Λ-theories, resp. of Λ=-theories with quotients into Λ=-theories. Each of the two inclusions is part of an adjunction whose right, resp. left, functor adds quotients for equivalence relations. After discussing the above adjunctions and their connection to logic and type theory, I shall present a recent result, obtained with Fabio Pasquali and Pino Rosolini, showing that the first embedding is 2-comonadic. Finally, if time allows, I shall delve into the connections to model theory and discuss how the comonadic adjuntion provides an algebraic description of Shelah’s construction of a theory that eliminates imaginaries from classical model theory. The talk is based on the paper E., Pasquali, Rosolini. Elementary doctrines as coalgebras. J. Pure Appl. Algebra 224, 2020. doi:10.1016/j.jpaa.2020.106445

The seminar will be held on Zoom. In order to get access to the Zoom meeting, please contact Peter Schuster.