{"paper":{"title":"Monoidal cofibrant resolutions of dg algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.KT","authors_text":"Boris Shoikhet","submitted_at":"2011-12-11T14:21:17Z","abstract_excerpt":"Let $k$ be a field of any characteristic. In this paper, we construct a functorial cofibrant resolution $\\mathfrak{R}(A)$ for the $\\mathbb{Z}_{\\le 0}$-graded dg algebras $A$ over $k$, such that the functor $A\\rightsquigarrow \\mathfrak{R}(A)$ is colax-monoidal with quasi-isomorphisms as the colax maps. More precisely, there are maps of bifunctors $\\mathfrak{R}(A\\otimes B)\\to \\mathfrak{R}(A)\\otimes \\mathfrak{R}(B)$, compatible with the projections to $A\\otimes B$, and obeying the colax-monoidal axiom.\n  The main application of such resolutions (which we consider in our next paper) is the existen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2360","kind":"arxiv","version":3},"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"}