Stable Categories and Structured Ring SpectraAndrew J. Blumberg, Teena Gerhardt, Michael A. Hill Cambridge University Press, 21.07.2022 - 450 Seiten This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors - Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk - offer a complete, authoritative source to learn the foundations of this vibrant area. |
Andere Ausgaben - Alle anzeigen
Stable Categories and Structured Ring Spectra Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill Eingeschränkte Leseprobe - 2022 |
Häufige Begriffe und Wortgruppen
abelian action adjoint adjunction admits algebras apply argument associated axioms CAlg called canonical classical closed cofibrant colimits commutative ring spectra complex composite condition connective consider construction corresponding define Definition denote derived functors diagram element enriched étale Example exists extension fact factorization fibrations finite formal full subcategory functor geometric given gives groups homology homotopy category homotopy groups homotopy theory identity implies inclusion induced invertible isomorphism issn lifting limits localization Math model category model structure modules morphisms multiplication natural Note notion O-algebra objects obtain operad orthogonal pair particular pointed presentable preserves projective Proof Proposition prove pushout R-module relations Remark replacement respect result satisfies sends sense sequence sheaves simplicial simplicial sets spaces spectrum stable symmetric monoidal tensor Theorem topological trivial underlying unique unit universal weak equivalences write