We give a model of restricted L_infinity-algebras in a nice preadditive symmetric monoidal infinity-category C as an algebra over the monad associated to an adjunction between C and the infinity-category of cocommutative bialgebras in C, where the left adjoint lifts the free associative algebra. If C is additive, we construct a canonical forgetful functor from restricted L_infinity-algebras in C to spectral Lie algebras in C and show that this functor is an equivalence if C is a Q-linear stable infinity-category. For every field K we construct a canonical forgetful functor from restricted L_infinity-algebras in connective K-module spectra to the infinity-category underlying a model structure on simplicial restricted Lie algebras over K.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-201909201996 |
| Date | 20 September 2019 |
| Creators | Heine, Hadrian |
| Contributors | Prof. Dr. Markus Spitzweck, Prof. Dr. Thomas Nikolaus |
| Source Sets | Universität Osnabrück |
| Language | German |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, application/zip |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Germany, http://creativecommons.org/licenses/by-nc-nd/3.0/de/ |
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