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Rings, Modules, and Algebras in Stable Homotopy Theory
Anthony Elmendorf,Michael Cole +1 more
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In this paper, the authors introduce the category of Structured ring and module spectra under $S$ and show how to construct a monadic bar construction on a function spectra.Abstract:
Introduction Prologue: the category of ${\mathbb L}$-spectra Structured ring and module spectra The homotopy theory of $R$-modules The algebraic theory of $R$-modules $R$-ring spectra and the specialization to $MU$ Algebraic $K$-theory of $S$-algebras $R$-algebras and topological model categories Bousfield localizations of $R$-modules and algebras Topological Hochschild homology and cohomology Some basic constructions on spectra Spaces of linear isometries and technical theorems The monadic bar construction Epilogue: The category of ${\mathbb L}$-spectra under $S$ Appendix A. Twisted half-smash products and function spectra Bibliography Index.read more
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Algebras and Modules in Monoidal Model Categories
Stefan Schwede,Brooke Shipley +1 more
TL;DR: In this paper, the authors provide a general method for constructing model category structures for categories of ring, algebra, and module spectra, and provide the necessary input for obtaining model categories of symmetric ring spectra and functors with smash product.
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Model categories of diagram spectra
TL;DR: In this article, the basic theory of diagram spaces and diagram spectra is given, and model structures on these categories are constructed and compared, with the caveat that -spaces are always connective.
Book
Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Bertrand Toën,Gabriele Vezzosi +1 more
TL;DR: In this article, the authors define a general notion of geometric stack over a base symmetric monoidal model category C, and prove that this notion satisfies the expected properties of the algebraic n-stacks of Simpson.
Book
Axiomatic stable homotopy theory
TL;DR: In this article, Smallness, limits and constructibility of stable homotopy theory are defined and a generalization of Bousfield localization has been proposed, including the notion of Brown representability.
References
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Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
Book
Basic concepts of enriched category theory
TL;DR: Lack, Ross Street and Wood as discussed by the authors present a mathematical subject classification of 18-02, 18-D10, 18D20, and 18D21 for mathematics subject classification.
Book
The geometry of iterated loop spaces
TL;DR: In this article, the recognition principle and A? spaces and E? spaces have been discussed and a categorical construction of monoidal categories has been proposed for simplicial spaces and infinite loop sequences.
Book
Simplicial objects in algebraic topology
TL;DR: Simplicial Objects in Algebraic Topology as discussed by the authors has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces.