Homotopical Properties of the Simplicial Maurer–Cartan Functor
| Autor: | Christopher L. Rogers |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Pure mathematics Fiber functor Functor Brown's representability theorem Model category 010102 general mathematics Cone (category theory) Mathematics::Algebraic Topology 01 natural sciences Simplicial homology Simplicial complex Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences Simplicial set 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | MATRIX Book Series ISBN: 9783319722986 |
| DOI: | 10.1007/978-3-319-72299-3_1 |
| Popis: | We consider the category whose objects are filtered, or complete, L ∞ -algebras and whose morphisms are ∞-morphisms which respect the filtrations. We then discuss the homotopical properties of the Getzler–Hinich simplicial Maurer–Cartan functor which associates to each filtered L ∞ -algebra a Kan simplicial set, or ∞-groupoid. In previous work with V. Dolgushev, we showed that this functor sends weak equivalences of filtered L ∞ -algebras to weak homotopy equivalences of simplicial sets. Here we sketch a proof of the fact that this functor also sends fibrations to Kan fibrations. To the best of our knowledge, only special cases of this result have previously appeared in the literature. As an application, we show how these facts concerning the simplicial Maurer–Cartan functor provide a simple ∞-categorical formulation of the Homotopy Transfer Theorem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|