A stable model category is a setting for homotopy theory where the suspension functor is
invertible. The prototypical examples are the category of spectra in the sense of stable …

We give two general constructions for the passage from unstable to stable homotopy that
apply to the known example of topological spaces, but also to new situations, such as the A …

Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits
of category theory, which can be approached either using classical explicit constructions or …

The core of classical homotopy theory is a body of ideas and theorems that emerged in the
1950s and was later largely codified in the notion of a model category. This core includes …

In this paper, we study Azumaya algebras and Brauer groups in derived algebraic geometry.
We establish various fundamental facts about Brauer groups in this setting, and we provide …

In the early 1970's, the theory of E1 rings was intrinsically intertwined with a host of
constructions and calculations that centered around the relationship between E1 ring …

This monograph introduces a framework for genuine proper equivariant stable homotopy
theory for Lie groups. The adjective 'proper'alludes to the feature that equivalences are …

We exhibit examples of triangulated categories which are neither the stable category of a
Frobenius category nor a full triangulated subcategory of the homotopy category of a stable …

Let K (n) be the nth Morava K-theory at a prime p, and let T (n) be the telescope of a vn-self
map of a finite complex of type n. In this paper we study the K (n)*-homology of Ω∞ X, the …