{"paper":{"title":"The infinity Quillen functor, Maurer-Cartan elements and DGL realizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Daniel Tanr\\'e, Urtzi Buijs, Yves F\\'elix","submitted_at":"2017-02-14T21:30:12Z","abstract_excerpt":"We show an alternative construction of the cosimplicial free complete diferential graded Lie algebra $\\mathfrak{L}_\\bullet=\\widehat{\\mathbb{L}}(s^{-1}\\Delta^\\bullet)$ based on a new Lie bracket formulae for Lie polynomials on a general tensor algebra. Based on it,we prove that for any complete differential graded Lie algebra $L$, its geometrical realization $\\langle L\\rangle=\\text{Hom}_{\\text{cdgl}}(\\mathfrak{L}_\\bullet,L)$ is isomorphic to its nerve $\\gamma_\\bullet(L)$, a deformation retract of the Getzler-Hinich realization $\\text{MC}(\\mathscr{A}_\\bullet\\widehat{\\otimes} L)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04397","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}