Alex Simpson: Independent pullbacks and monoidal structure

Abstract: Independent pullback structure is a simple category-theoretic structure that embraces several distinct mathematical notions of conditional independence. In this talk, I shall explore various interactions between independent pullback structure and monoidal structure. These interactions will take us on a tour involving semicartesian categories, promonoidal categories, Day convolution and Day's reflection theorem, all topics that are of general category-theoretic interest.

In the second half of the talk, I shall look at fibred monoidal structure. At the presheaf level, a crucial role is played by the notion of presheaf with supports, a property that turns out to enjoy a subtle interrelationship with the property of being a sheaf for the atomic Grothendieck topology.

Joint work with Timothée Bonnefoi (Antwerp), Berend van Starkenburg (Leiden) and Dario Stein (Nijmegen).