activity
20042026
most citedMonads with arities and their associated theories

80 citations · 164 across the 15 of their papers we have counts for

collaborators

18 papers

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.CT2025

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…

math.CT2019

Every 2-Segal space is unital

Matthew Feller, Richard Garner, Joachim Kock +2

We prove that every 2-Segal space is unital.

math.CT2018★ 6 cited

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…

math.CT2016★ 7 cited

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…

math.CT2015

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…