We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact k-linear monoidal functor can be lifted to a tensor equivalence under some certain conditions.

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Yuying Xu is currently a PhD student at Nanjing University and University of Stuttgart.

Related work: "On the stable equivalences between finite tensor categories", Yuying Xu and Gongxiang Liu, Proc. Amer. Math. Soc. 151 (2023), 1867-1876

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