1 citations · 2 across the 5 of their papers we have counts for
5 papers
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…
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 order-p…
Convex decomposition spaces and Crapo complementation formula
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We establish a Crapo complementation formula for the Möbius function in a general decomposition space in terms of a convex subspace and its complement: $μ^X \simeq μ^…
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…
Decomposition Spaces, Incidence Algebras and Möbius Inversion
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We introduce the notion of decomposition space as a general framework for incidence algebras and Möbius inversion: it is a simplicial infinity-groupoid satisfying an exactness cond…