Simplicial Methods for Operads and Algebraic Geometry

• Main Authors: Moerdijk, Ieke (Author), Toën, Bertrand (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2010.
• Series: Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Mathematics.; Category theory (Mathematics).; Homological algebra.; Algebraic topology.; Category Theory, Homological Algebra.; Algebraic Topology.

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 operad...

Table of Contents:

• 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.