We define and investigate a class of categories with formal properties similar to those of the
homotopy category of spectra. This class includes suitable versions of the derived category …

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 …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

About two decades ago, Tom Goodwillie began formulating his calculus of homotopy
functors as a way to organize and understand arguments being used by him and others in …

The notion of quasi-category was introduced by Boardman and Vogt in their work on
homotopy invariant algebraic structures [BV]. A Kan complex and the nerve of a category are …

The bulk of this paper is devoted to the comparison of several models for the theory of
(infinity, 2)-categories: that is, higher categories in which all k-morphisms are invertible for k> …

In this paper we advertise the category of Γ-spaces as a convenient framework for doing
'algebra'over 'rings' in stable homotopy theory. Γ-spaces were introduced by Segal [Se] who …

arXiv:0905.0459v1 [math.CT] 4 May 2009 Page 1 arXiv:0905.0459v1 [math.CT] 4 May 2009
Derived Algebraic Geometry V: Structured Spaces May 5, 2009 Contents 1 Structure Sheaves …

We define a simplicial category called the category of derived manifolds. It contains the
category of smooth manifolds as a full discrete subcategory, and it is closed under taking …