147 citations · 550 across the 42 of their papers we have counts for
49 papers
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…
Culf maps and edgewise subdivision
Philip Hackney, Joachim Kock
We show that, for any simplicial space , the -category of culf maps over is equivalent to the -category of right fibrations over , the…
-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…
Tracelet Hopf Algebras and Decomposition Spaces (Extended Abstract)
Nicolas Behr, Joachim Kock
Tracelets are the intrinsic carriers of causal information in categorical rewriting systems. In this work, we assemble tracelets into a symmetric monoidal decomposition space, indu…
Whole-grain Petri nets and processes
Joachim Kock
We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz an…
The incidence comodule bialgebra of the Baez-Dolan construction
Joachim Kock
Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez--Dolan construction on P. These two new operads have the same space of…