147 citations · 550 across the 42 of their papers we have counts for
6 papers · 1 filter
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…
Cospan construction of the graph category of Borisov and Manin
Joachim Kock
It is shown how the graph category of Borisov and Manin can be constructed from (a variant of) the graph category of Joyal and Kock, essentially by reversing the generic morphisms.…
Graphs, hypergraphs, and properads
Joachim Kock
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad mon…
Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
Imma Galvez-Carrillo, Joachim Kock, Andrew Tonks
We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equ…
Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract)
André Joyal, Joachim Kock
We describe a category of Feynman graphs and show how it relates to compact symmetric multicategories (coloured modular operads) just as linear orders relate to categories and root…
Polynomial functors and opetopes
Joachim Kock, André Joyal, Michael Batanin +1
We give an elementary and direct combinatorial definition of opetopes in terms of trees, well-suited for graphical manipulation and explicit computation. To relate our definition t…