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Simplicial Methods for Operads and Algebraic Geometry
This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijk's lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of o...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2010.
|
| Edición: | 1st ed. 2010. |
| Colección: | Advanced Courses in Mathematics - CRM Barcelona,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-0348-0052-5 | ||
| 003 | DE-He213 | ||
| 005 | 20220117031834.0 | ||
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| 020 | |a 9783034800525 |9 978-3-0348-0052-5 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0052-5 |2 doi | |
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| 082 | 0 | 4 | |a 512.6 |2 23 |
| 100 | 1 | |a Moerdijk, Ieke. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Simplicial Methods for Operads and Algebraic Geometry |h [electronic resource] / |c by Ieke Moerdijk, Bertrand Toën. |
| 250 | |a 1st ed. 2010. | ||
| 264 | 1 | |a Basel : |b Springer Basel : |b Imprint: Birkhäuser, |c 2010. | |
| 300 | |a X, 186 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Advanced Courses in Mathematics - CRM Barcelona, |x 2297-0312 | |
| 505 | 0 | |a Lectures on Dendroidal Sets -- Operads -- Trees as operads -- Dendroidal sets -- Tensor product of dendroidal sets -- A Reedy model structure on dendroidal spaces -- Boardman-Vogt resolution and homotopy coherent nerve -- Inner Kan complexes and normal dendroidal sets -- Model structures on dendroidal sets -- Simplicial Presheaves and Derived Algebraic Geometry -- Motivation and objectives -- Simplicial presheaves as stacks -- Algebraic stacks -- Simplicial commutative algebras -- Derived stacks and derived algebraic stacks -- Examples of derived algebraic stacks. | |
| 520 | |a This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijk's lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena. For example, dendroidal sets admit a closed symmetric monoidal structure related to the Boardman-Vogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with a suitable model structure on the category of dendroidal sets. Important concepts are illustrated with pictures and examples. The lecture series by Toën presents derived algebraic geometry. While classical algebraic geometry studies functors from the category of commutative rings to the category of sets, derived algebraic geometry is concerned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derived quotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent condition. These lectures provide a concise and focused introduction to this vast subject, glossing over many of the technicalities that make the subject's research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Toën's lectures, some background in algebraic geometry is also necessary. | ||
| 650 | 0 | |a Algebra, Homological. | |
| 650 | 0 | |a Algebraic topology. | |
| 650 | 1 | 4 | |a Category Theory, Homological Algebra. |
| 650 | 2 | 4 | |a Algebraic Topology. |
| 700 | 1 | |a Toën, Bertrand. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783034800518 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034800532 |
| 830 | 0 | |a Advanced Courses in Mathematics - CRM Barcelona, |x 2297-0312 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-0348-0052-5 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||