Model categories are used as a tool for inverting certain maps in a category in a controllable
manner. They are useful in diverse areas of mathematics. This book offers a comprehensive …

The stable homotopy category, much studied by algebraic topologists, is a closed symmetric
monoidal category. For many years, however, there has been no well-behaved closed …

In recent years the theory of structured ring spectra (formerly known as A-and E-ring spectra)
has been simplified by the discovery of categories of spectra with strictly associative and …

We define the spectrum of a tensor triangulated category as the set of so-called prime ideals,
endowed with a suitable topology. In this very generality, the spectrum is the universal space …

We study the interaction between geometric operations on stacks and algebraic operations
on their categories of sheaves. We work in the general setting of derived algebraic …

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 …

for a noetherian scheme, we introduce its unbounded stable derived category. this leads to a
recollement which reflects the passage from the bounded derived category of coherent …

The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

This book develops rigorous foundations for parametrized homotopy theory, which is the
algebraic topology of spaces and spectra that are continuously parametrized by the points of …

We make a general study of Quillen model structures on abelian categories. We show that
they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have …