64 citations · 158 across the 9 of their papers we have counts for
9 papers
Gabriel-Zisman Cohomology and spectral sequences
Imma Gálvez-Carrillo, Frank Neumann, Andrew Tonks
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by f…
Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation
Imma Gálvez-Carrillo, Ralph M. Kaufmann, Andrew Tonks
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for m…
Decomposition spaces and restriction species
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We show that Schmitt's restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated…
Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
Imma Gálvez-Carrillo, Ralph M. Kaufmann, Andrew Tonks
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for m…
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…
An A-infinity operad in spineless cacti
Imma Gálvez-Carrillo, Leandro Lombardi, Andrew Tonks
The d.g. operad C of cellular chains on the operad of spineless cacti is isomorphic to the Gerstenhaber-Voronov operad codifying the cup product and brace operations on the Hochsch…
André spectral sequences for Baues-Wirsching cohomology of categories
Imma Gálvez-Carrillo, Frank Neumann, Andrew Tonks
We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendiec…