Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Nate Bottman
Affiliation:

MPIM
Date:

Tue, 24/05/2022 - 13:45 - 15:30 For zoom details contact: Gaetan Borot (gaetan.borot@hu-berlin.de)

The Barrâ€“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 Abouzaidâ€™s generation criterion, and we hope that it will be a useful tool in the computation of Fukaya categories.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/10472