3 papers
math.CT2026
Pita factorisation in operadic categories
Michael Batanin, Joachim Kock, Mark Weber
In strictly factorisable operadic categories, every morphism factors uniquely as where is order-preserving and is a quasibijection that is ord…
math.CT2026
Operadic categories as (pseudo)-simplicial groupoids
Michael Batanin, Joachim Kock, Mark Weber
From any operadic category O we construct a simplicial groupoid X (slightly pseudo in a specific way), called the operadic nerve. It integrates all the structure of chosen-local-te…
math.CO2025
Noncrossing arithmetic
Kurusch Ebrahimi-Fard, Loïc Foissy, Joachim Kock +1
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory…