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The Barr-Beck Theorem in Symplectic Geometry

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Nate Bottman
Tue, 24/05/2022 - 13:45 - 15:30

For zoom details contact: Gaetan Borot (

The Barr–Beck theorem gives conditions under which an adjunction F -| G is monadic. Monadicity, in turn, means that the category on the right can be computed in terms of the data of F and its endomorphism GF. I will present joint work-in-progress with Abouzaid, in which we consider this theorem in the case of the functors between Fuk(M1) and Fuk(M2) associated to a Lagrangian correspondence L12 and its transpose. These functors are often adjoint, and under the hypothesis that a certain map to symplectic cohomology hits the unit, the hypotheses of Barr-Beck are satisfied. This can be interpreted as an extension of Abouzaid’s generation criterion, and we hope that it will be a useful tool in the computation of Fukaya categories.

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