Simplicial methods for operads and algebraic geometry
著者
書誌事項
Simplicial methods for operads and algebraic geometry
（Advanced courses in mathematics CRM Barcelona）
Birkhäuser , Springer, c2010
- : pbk
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内容説明・目次
内容説明
This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures - livered at the Centre de Recerca Matem ati ca in February 2008, as part of a special year on Homotopy Theory and Higher Categories. Ieke Moerdijk's lectures constitute an introduction to the theory ofdendroidal sets, an extension of the theory of simplicial sets designed as a foundation for the homotopy theory of operads. The theory has many features analogous to the theory of simplicial sets, but it also reveals many new phenomena, thanks to the presence of automorphisms of trees. Dendroidal sets admit a closed symmetric monoidal structure related to the Boardman{Vogt tensor product. The lecture notes develop the theory very carefully, starting from scratch with the combinatorics of trees, and culminating with a model structure on the category of dendroidal sets for which the brant objects are the inner Kan dendroidal sets. The important concepts are illustrated with detailed examples.
目次
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.
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