147 citations · 550 across the 42 of their papers we have counts for
24 papers · 1 filter
Free decomposition spaces
Philip Hackney, Joachim Kock
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon…
-operads as symmetric monoidal -categories
Rune Haugseng, Joachim Kock
We use Lurie's symmetric monoidal envelope functor to give two new descriptions of -operads: as certain symmetric monoidal -categories whose underlying symmetric mo…
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…
Decomposition-space slices are toposes
Joachim Kock, David I. Spivak
We show that the category of decomposition spaces and CULF maps is locally a topos. Precisely, the slice category over any decomposition space D is a presheaf topos, namely decomp/…
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…