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 …

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 …

We show that the homotopy theory of differential graded algebras coincides with the
homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences …

The purpose of this paper is to describe a connection between model categories, a structure
invented by algebraic topologists that allows one to introduce the ideas of homotopy theory …

This textbook is an introduction to the modern foundations of stable homotopy theory and
'algebra'over structured ring spectra, based on symmetric spectra. We begin with a quick …

We show how methods from K-theory of operator algebras can be applied in a completely
algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive K-theory of …

In this paper, we present an infinity-categorical version of the theory of monoidal categories.
We show that the infinity category of spectra admits an essentially unique monoidal structure …

Given a finite group G we show that Dress and Siebeneicher's ring of G‐typical Witt vectors
on the Lazard ring, that is, on the polynomial ring on countably many indeterminates over …

Let $ L $ and $ N $ be two smooth manifolds of the same dimension. Let $ j\colon L\to T^* N
$ be an exact Lagrange embedding. We denote the free loop space of $ X $ by $\Lambda X …

We investigate the relationship between differential graded algebras (dgas) and topological
ring spectra. Every dga C gives rise to an Eilenberg–Mac Lane ring spectrum denoted HC. If …