Tuesday, October 15, 14:00, 7.527.

Yuying Xu
Equivalences of Tensor Triangulated Categories - Stable Tensor Equivalences and Derived Tensor Equivalences I, II.

Abstract:
This talk focuses on the stable categories of finite tensor categories and the derived categories of finite tensor categories which are tensor triangulated categories. We look for relations between tensor equivalences, stable tensor equivalences and derived tensor equivalences. Our first two main results show that a stable tensor equivalence induces a tensor equivalence under certain conditions. Later on, we have used monoidal t-structures to prove that a derived tensor equivalence always induces a tensor equivalence. And a derived tensor equivalence induces a stable tensor equivalence.

The first part is joint work with Gongxiang Liu and the second part is ongoing joint work with Junhua Zheng.