THH and traces of enriched categories

TL;DR

This paper presents a universal construction of topological Hochschild homology (THH) for enriched infinity categories using a presheaf of circles, grounded in a model-independent framework for enriched higher category theory.

Contribution

It introduces a novel, universal approach to constructing THH for enriched infinity categories via presheaves, supported by a new elementary framework for enriched higher categories.

Findings

THH can be obtained from a presheaf of circles on a combinatorial category.

The framework for enriched higher categories is elementary and model-independent.

The approach provides a universal construction applicable to any enriched infinity category.

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 infinity category. Our results rely crucially on an elementary, model-independent framework for enriched higher category theory, which may be of independent interest.