80 citations · 164 across the 15 of their papers we have counts for
18 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…
Every 2-Segal space is unital
Matthew Feller, Richard Garner, Joachim Kock +2
We prove that every 2-Segal space is unital.
Operadic categories and décalage
Richard Garner, Joachim Kock, Mark Weber
Batanin and Markl's operadic categories are categories in which each map is endowed with a finite collection of "abstract fibres" -- also objects of the same category -- subject to…
Faà di Bruno for operads and internal algebras
Joachim Kock, Mark Weber
For any coloured operad R, we prove a Faà di Bruno formula for the `connected Green function' in the incidence bialgebra of R. This generalises on one hand the classical Faà di Bru…
Algebraic Kan extensions along morphisms of internal algebra classifiers
Mark Weber
An algebraic left Kan extension is a left Kan extension which interacts well with the algebraic structure present in the given situation, and these appear in various subjects such…