Thomas Jan Mikhail

most citedFuzzy simplicial sets and their application to geometric data analysis

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math.CT2025

A type-theoretic definition of lax $(\infty, \infty)$ -limits

Thomas Jan Mikhail

We introduce and study a purely syntactic notion of lax cones and $(\infty, \infty)$ -limits on finite computads in \texttt{CaTT}, a type theory for $(\infty, \infty)$ -categories due…

math.CT2025

Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence

Joachim Kock, Thomas Jan Mikhail

A theorem of Bergner, Osorno, Ozornova, Rovelli, and Scheimbauer states an equivalence between 2-Segal spaces and certain augmented stable double Segal spaces. In this paper we est…

A type-theoretic definition of lax (∞,∞)-limits

Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence

A type-theoretic definition of lax $(\infty, \infty)$ -limits