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Elementary doctrines as coalgebras

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If you have a question about this talk, please contact Benedikt Ahrens.

Lawvere’s hyperdoctrines mark the beginning of applications of category theory to logic. In particular, elementary doctrines provide an algebraic framework to deal with logics with equality. The connection between (typed) logical theories and certain Pos-valued functors is exemplified by two embeddings: of elementary doctrines into primary ones, and of elementary doctrines with effective quotients into elementary ones. Each of the two inclusions is part of an adjunction whose right, resp. left, functor freely adds quotients for equivalence relations. After discussing the above adjunctions and their connection to logic, I shall present a recent result, obtained with Fabio Pasquali and Pino Rosolini, showing that the first embedding is 2-comonadic. Finally, I shall discuss how this framework can be used to obtain an algebraic description of Shelah’s construction of a theory that eliminates imaginaries from classical model theory.

This talk is part of the Theoretical computer science seminar series.

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