23 citations · 33 across the 10 of their papers we have counts for
12 papers
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…
Inverse limits of left adjoint functors on pointed sets
Ilan Barnea, Saharon Shelah
This paper is a continuation of [BaSh], where we studied the behaviour of the abelianization functor under inverse limits. Our main result in [BaSh] was that if is a…
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 abelianization of inverse limits of groups
Ilan Barnea, Saharon Shelah
The abelianization is a functor from groups to abelian groups, which is left adjoint to the inclusion functor. Being a left adjoint, the abelianization functor commutes with all sm…
Model structure on projective systems of -algebras and bivariant homology theories
Ilan Barnea, Michael Joachim, Snigdhayan Mahanta
Using the machinery of weak fibration categories due to Schlank and the first author, we construct a convenient model structure on the pro-category of separable -algebras $\ma…
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…
Model Structures on Ind Categories and the Accessibility Rank of Weak Equivalences
Ilan Barnea, Tomer M. Schlank
In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak f…
A new model for pro-categories
Ilan Barnea, Tomer M. Schlank
In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications…
Functorial Factorizations in Pro Categories
Ilan Barnea, Tomer M. Schlank
In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the exi…
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…