64 citations · 361 across the 27 of their papers we have counts for
6 papers · 1 filter
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…
Thomason cohomology of categories
Imma Galvez-Carrillo, Frank Neumann, Andrew Tonks
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at…
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…
On determinant functors and -theory
Fernando Muro, Andrew Tonks, Malte Witte
In this paper we introduce a new approach to determinant functors which allows us to extend Deligne's determinant functors for exact categories to Waldhausen categories, (strongly)…
On K_1 of a Waldhausen category
Fernando Muro, Andrew Tonks
We give a simple representation of all elements in K_1 of a Waldhausen category and prove relations between these representatives which hold in K_1.
The 1-type of a Waldhausen K-theory spectrum
Fernando Muro, Andrew Tonks
We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicati…