Localization of algebras over coloured operads

C. Casacuberta, J. J. Gutiérrez, I. Moerdijk, R. M. Vogt

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    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 maps between ring spectra, 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.
    Original languageEnglish
    Pages (from-to)105-136
    Number of pages32
    JournalProceedings of the London Mathematical Society
    Volume101
    Issue number1
    DOIs
    Publication statusPublished - 2010

    Fingerprint

    Dive into the research topics of 'Localization of algebras over coloured operads'. Together they form a unique fingerprint.

    Cite this