23 citations · 33 across the 10 of their papers we have counts for
6 papers · 1 filter
Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra
Gregory Arone, Ilan Barnea, Tomer M. Schlank
In a companion paper [ABS1] we introduced the stable -category of noncommutative CW-spectra, which we denoted . Let denote the full spectrally e…
Noncommutative CW-spectra as enriched presheaves on matrix algebras
Gregory Arone, Ilan Barnea, Tomer M. Schlank
Motivated by the philosophy that -algebras reflect noncommutative topology, we investigate the stable homotopy theory of the (opposite) category of -algebras. We focus on…
From weak cofibration categories to model categories
Ilan Barnea, Tomer M. Schlank
In [BaSc2] the authors introduced a much weaker homotopical structure than a model category, called a "weak cofibration category". We further showed that a small weak cofibration c…
The two out of three property in ind-categories and a convenient model category of spaces
Ilan Barnea
In [BaSc2], the author and Tomer Schlank introduced a much weaker homotopical structure than a model category, which we called a "weak cofibration category". We further showed that…
Pro-categories in homotopy theory
Ilan Barnea, Yonatan Harpaz, Geoffroy Horel
The goal of this paper is to prove an equivalence between the model categorical approach to pro-categories, as studied by Isaksen, Schlank and the first author, and the -ca…
A Projective Model Structure on Pro Simplicial Sheaves, and the Relative Étale Homotopy Type
Ilan Barnea, Tomer M. Schlank
In this work we shall introduce a new model structure on the category of pro-simplicial sheaves, which is very convenient for the study of étale homotopy. Using this model structur…