The Trace Field Theory of a Finite Tensor Category

Given a finite tensor category $\mathcal {C}$ , we prove that modified trace on the ideal of projective objects can be obtained from suitable trivialization Nakayama functor as right -module functor. Using result Costello, this allows us to associate any equipped with such chain complex valued topological conformal field theory, theory. The theory topologically describes trace, Hattori-Stallings and also structures induced by them Hochschild . In article, focus implications in linear (as opposed differential graded) setting: We use define non-unital homotopy commutative product chains degree zero. This is block diagonal described through handle elements Taking recovers Cartan matrix