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Pro-categories in homotopy theory

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 $\infty$-categorical approach,…
arXiv (opens in a new tab)

A Projective Model Structure on Pro Simplicial Sheaves, and the Relative \'Etale Homotopy Type

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 \'etale homotopy. Using this model structure we define a…
arXiv (opens in a new tab)

Noncommutative CW-spectra as enriched presheaves on matrix algebras

Motivated by the philosophy that C∗-algebras reflect noncommutative topology, we investigate the stable homotopy theory of the (opposite) category of C∗-algebras. We focus on C∗-algebras which are…
arXiv (opens in a new tab)

A new model for pro-categories

A new way to construct the pro-category of a category is presented, which solves an open problem of Isaksen [Isa] concerning the existence of functorial factorizations in what is known as the strict model structure on a pro- category.
arXiv (opens in a new tab)

The two out of three property in ind-categories and a convenient model category of spaces

In recent work, the author and Tomer Schlank introduced a much weaker structure than a model category, which we called a "weak cofibration category." We further showed that a small weak cofibration…
arXiv (opens in a new tab)

Functorial Factorizations in Pro Categories

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 existence of certain…
arXiv (opens in a new tab)

The abelianization of inverse limits of groups

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 small colimits. In…
Springer Nature (opens in a new tab)

Model Structures on Ind Categories and the Accessibility Rank of Weak Equivalences

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 fibration category…
arXiv (opens in a new tab)

From weak cofibration categories to model categories

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 category induces in…
arXiv (opens in a new tab)

Model structure on projective systems of $C^*$-algebras and bivariant homology theories

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 $C^*$-algebras…
arXiv (opens in a new tab)
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