3 papers
math.AT2025
Free loop spaces and the Cauchy--Frobenius Lemma
Joachim Kock, Thomas Jan Mikhail
We upgrade the Cauchy--Frobenius Lemma (`Burnside's Lemma') to a homotopy equivalence of -groupoids, essentially given by double counting/Fubini in the free loop space of t…
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…
math.CT2024
A type-theoretic definition of lax -limits
Thomas Jan Mikhail
We introduce and study a purely syntactic notion of lax cones and -limits on finite computads in \texttt{CaTT}, a type theory for -categories due…