THH and Traces of Enriched Categories

Abstract

We prove that topological Hochschild homology (THH) arises from a presheaf of circles on a certain combinatorial category, which gives a universal construction of THH for any enriched $\infty $-category. Our results rely crucially on an elementary, model-independent framework for enriched higher-category theory, which may be of independent interest. For those interested only in enriched category theory, read Sections 1.3 and 2.

Enriched infinity categories I: enriched presheaves

“…Remark 3.3. In [3], we call the active morphisms in Assoc S bypass operations, and we study the symmetric monoidal envelope of Assoc S , which we call Bypass S .…”