Tensor triangulated categories have recently gained attention as an object of study in algebraic geometry, representation theory, and homotopy theory. In this talk we will discuss a deformation theory of these structures inspired by the deformation theory of tensor categories due to Davydov and Yetter which deforms the structural coherence data of the monoidal structure on such a category. To do this, we will exploit the Morita theorem for dg-categories and encode tensor structures in terms of a certain kind of dg-bimodules which we will then use to define a Davydov-Yetter complex of which its total cohomology can be seen to contain data of the infinitesimal first order deformations of the associativity data of our tensor triangulated categories.
Zoom link: https://icts-res-in.zoom.us/j/91960656376?pwd=K0lNT1JsbjRzenljY2k3blBOUUgwdz09
Meeting ID: 919 6065 6376
Passcode: 869238