Derived Algebraic Geometry II: Noncommutative Algebra release_4ojzhptbwndndjaz3bsptxeoce

by Jacob Lurie

Released as a article .

2007  

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.
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Type  article
Stage   submitted
Date   2007-02-11
Version   v1
Language   en ?
arXiv  math/0702299v1
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