Riemann–roch theorems in monoidal 2-categories

Abstract Smooth and proper dg-algebras have an Euler class valued in the Hochschild homology of algebra. This is worthy this name since it satisfies many familiar properties including compatibility with pairing on algebra that its opposite. Riemann–Roch theorems [21, 14]. In paper, we prove a broad generalization these theorems. We generalize from bicategory their bimodules to symmetric monoidal bicategories traces non-identity maps. Our also implies spectral regard result as instantiation 2-dimensional generalized cobordism hypothesis. perspective draws close others results about characteristics classes bicategorical traces.