{"paper":{"title":"Homotopical Algebra in Categories with Enough Projectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Ged Corob Cook","submitted_at":"2017-03-02T01:00:17Z","abstract_excerpt":"For a complete and cocomplete category $\\mathcal{C}$ with a well-behaved class of `projectives' $\\bar{\\mathcal{P}}$, we construct a model structure on the category $s\\mathcal{C}$ of simplicial objects in $\\mathcal{C}$ where the weak equivalences, fibrations and cofibrations are defined in terms of $\\bar{\\mathcal{P}}$. This holds in particular when $\\mathcal{C}$ is $\\mathcal{U}$, the category of compactly generated, weakly Hausdorff spaces, and $\\bar{\\mathcal{P}}$ is the class of compact Hausdorff spaces.\n  We also construct a new model structure on $\\mathcal{U}$ itself, where the cofibrant spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00569","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"}