{"paper":{"title":"Modular Model Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Renaud Gauthier","submitted_at":"2019-06-22T20:14:40Z","abstract_excerpt":"To any model category $\\mathcal{M}$, we associate a modular model category, a functor of points $\\mathcal{M}[-]:$ Cat $\\rightarrow$ Cat, that associates to any small category $\\mathcal{C}$ a functor category $\\mathcal{M}[\\mathcal{C}] = \\text{Fun}_{fes}(\\mathcal{C}, \\mathcal{M})$ of full and essentially surjective functors from $\\mathcal{C}$ to $\\mathcal{M}$, providing parametrizations of a same model category $\\mathcal{M}$ by different small categories. We are in particular interested in using schemes as parameters. We consider $\\mathbb{Z}$Sm$/k$ the category of linear combinations of smooth s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09496","kind":"arxiv","version":1},"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"}