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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^…
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…