Localization of algebras over coloured operads
| Autor: | Casacuberta, C., Gutiérrez, J. J., Moerdijk, I., Vogt, R. M., Algebra & Geometry and Mathematical Locic, Sub Algebra,Geometry&Mathem. Logic begr. |
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| Přispěvatelé: | Centre de Recerca Matemàtica |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Pure mathematics
Ring (mathematics) Functor General Mathematics Homotopy Homotopia Context (language use) Mathematics - Category Theory Commutative ring Mathematics::Algebraic Topology Loop (topology) Categories (Matemàtica) Infinite loop Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) Category Theory (math.CT) Mathematics - Algebraic Topology 515.1 - Topologia Algebra over a field 55P43 18D50 55P60 Mathematics |
| Zdroj: | Proceedings of the London Mathematical Society, 101(1), 105. Oxford University Press Recercat. Dipósit de la Recerca de Catalunya instname |
| ISSN: | 0024-6115 |
| Popis: | We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical localizations preserve ring spectra (in the strict sense, not only up to homotopy), modules over ring spectra, and algebras over commutative ring spectra, as well as ring maps, module maps, and algebra maps. It is principally the treatment of module spectra and their maps that led us to the use of coloured operads (also called enriched multicategories) in this context. Comment: 34 pages |
| Databáze: | OpenAIRE |
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