Derived Algebraic Geometry II: Noncommutative Algebra
Category Theory
2007-09-19 v5 Algebraic Topology
Abstract
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 (such that the tensor product preserves colimits in each variable), and thereby recover the classical smash-product operation on spectra. We develop a general theory of algebras in a monoidal infinity category, which we use to (re)prove some basic results in the theory of associative ring spectra. We also develop an infinity-categorical theory of monads, and prove a version of the Barr-Beck theorem.
Cite
@article{arxiv.math/0702299,
title = {Derived Algebraic Geometry II: Noncommutative Algebra},
author = {Jacob Lurie},
journal= {arXiv preprint arXiv:math/0702299},
year = {2007}
}
Comments
170 pages; corrected some erroneous claims about the category of symmetric spectra, other minor changes. 9/19/07: minor modifications