![]() ![]() To this Calabi-Yau structure on Proj C, Costello's Theorem associates a topological conformal field theory Φ C that we refer to as the trace field theory of the finite tensor category C with symmetric Frobenius structure. Then the trace coming from this particular trivialization of N r produces, as discussed above, a Calabi-Yau structure on the tensor ideal Proj C ⊂ C. Instead, we are motivated by two-dimensional topological conformal field theory, a certain type of differential graded two-dimensional open-closed topological field theory: Suppose that we are given a finite tensor category C and a symmetric Frobenius structure, by which we mean a certain trivialization of the right Nakayama functor as right C-module functor relative to a pivotal structure (we give the details in Definition 4.6 it will amount to a pivotal structure and a trivialization of the distinguished invertible object). ![]()
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