{"paper":{"title":"Algebraic weak factorisation systems I: accessible AWFS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"John Bourke, Richard Garner","submitted_at":"2014-12-19T23:28:43Z","abstract_excerpt":"Algebraic weak factorisation systems (AWFS) refine weak factorisation systems by requiring that the assignations sending a map to its first and second factors should underlie an interacting comonad--monad pair on the arrow category. We provide a comprehensive treatment of the basic theory of AWFS---drawing on work of previous authors---and complete the theory with two main new results. The first provides a characterisation of AWFS and their morphisms in terms of their double categories of left or right maps. The second concerns a notion of cofibrant generation of an AWFS by a small double cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6559","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"}