We construct symmetric monoidal higher categories of iterated Calabi-Yau cospans, that are noncommutative analogs of iterated lagrangian correspondences. We actually give a general (and functorial) procedure that applies to iterated nondegenerate cospans on certain comma categories. This allows us to factor the AKSZ fully extended TFT associated with the moduli of objects of a Calabi-Yau category (taking values in iterated lagrangian correspondences) through a fully extended TFT taking values in iterated Calabi-Yau cospans.