This paper concerns open, closed, and open-closed topological conformal field theories. We show that the category of open topological conformal field theories, at all genera, is homotopy equivalent to a category of Calabi-Yau A∞ categories. For each such, we show that there is a universal closed TCFT, which is the initial element in the category of compatible open-closed TCFTs. The homology of ...

There is a very close and well-understood relationship between proofs in intuitionistic logic, simply typed lambda-terms, and morphisms in Cartesian closed categories. The same relationship can be established for multiplicative linear logic (MLL), where proof nets take the role of the lambda-terms, and starautonomous categories the role of Cartesian closed categories. It is certainly desirable ...