147 citations · 550 across the 42 of their papers we have counts for
6 papers · 1 filter
Combinatorial Dyson-Schwinger equations and inductive data types
Joachim Kock
The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The con…
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
Decomposition spaces are simplicial -groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF fun…
Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coeffi…
Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities a…
Polynomial functors and combinatorial Dyson-Schwinger equations
Joachim Kock
We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally…
Regular patterns, substitudes, Feynman categories and operads
Michael Batanin, Joachim Kock, Mark Weber
We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-category of substitudes of Day and Street (2003), and that the Feynman categories of Kau…