{"paper":{"title":"What do homotopy algebras form?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RA"],"primary_cat":"math.CT","authors_text":"Alexander E. Hoffnung, Christopher L. Rogers, Vasily A. Dolgushev","submitted_at":"2014-06-06T17:29:48Z","abstract_excerpt":"In paper arXiv:1406.1744, we constructed a symmetric monoidal category $LIE^{MC}$ whose objects are shifted (and filtered) L-infinity algebras. Here, we fix a cooperad $C$ and show that algebras over the operad $Cobar(C)$ naturally form a category enriched over $LIE^{MC}$. Following arXiv:1406.1744, we \"integrate\" this $LIE^{MC}$-enriched category to a simplicial category $HoAlg^{\\Delta}_C$ whose mapping spaces are Kan complexes. The simplicial category $HoAlg^{\\Delta}_C$ gives us a particularly nice model of an $(\\infty,1)$-category of $Cobar(C)$-algebras. We show that the homotopy category o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1751","kind":"arxiv","version":4},"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"}