Shadows are Bicategorical Traces

Abstract

The theory of shadows is an axiomatic, bicategorical framework that generalizes topological Hochschild homology (THH) and satisfies analogous important properties, such as Morita invariance. Using Berman's extension of THH to bicategories, we prove that there is an equivalence between functors out of THH of a bicategory and shadows on that bicategory. As an application we provide a new, conceptual proof that shadows are Morita invariant.

Riemann-Roch theorems in monoidal 2-categories

“…Thanks to recent work of Hess and Rasekh [HR21] this metatheorem is a theorem, and so the metatheorem from the beginning of introduction becomes something close to a theorem as long as the manipulations done with Hochschild homology only rely on formal properties of shadows.…”