Higher category theory

I work on enriched ∞-categories and ∞-operads, and on the use of enrichment to study (∞, n)-categories. In particular, I am interested in descriptions of enriched structures through presentable categories, as well as weighted colimits, profunctors, and Cauchy-completion.

Enriched categories and operads

With David Reutter, I describe enriched ∞-categories in terms of their enriched presheaf categories together with a marking by representable presheaves. This leads to constructions of tensor products and a model-independent description of univalence.

My work on enriched ∞-operads gives a corresponding description through marked presentably symmetric monoidal module categories. For enrichment in spaces, it recovers Lurie’s ∞-operads, including their envelopes and categories of algebras.

• Enriched ∞-categories as marked module categories — with David Reutter, 2025.
• Enriched ∞-operads as marked algebras — 2026.

Cauchy-completion

Cauchy-completeness unifies notions such as idempotent-completeness, additivity, and stability, depending on the enrichment. My work develops weighted-colimit and profunctor methods to study this construction and its iteration through higher categorical levels.

Applications to full dualizability are discussed on the fusion categories and TFTs page and in my doctoral thesis.

Notes on Cauchy-complete categories, profunctors, and lax additivity.