{"paper":{"title":"On the chain rule in Goodwillie calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Max Blans, Thomas Blom","submitted_at":"2024-10-27T16:38:42Z","abstract_excerpt":"We prove a generalization of the Arone-Ching chain rule for Goodwillie derivatives by showing that for any pair of reduced finitary functors $F \\colon \\mathcal{D} \\to \\mathcal{E}$ and $G \\colon \\mathcal{C} \\to \\mathcal{D}$ between differentiable $\\infty$-categories, there is an equivalence $\\partial_*(FG) \\simeq \\partial_*F \\circ_{\\partial_*{\\mathrm{id}_{\\mathcal{D}}}} \\partial_*G$. This confirms a conjecture of Lurie. The proof of this theorem consists of two parts, which are of independent interest. We first show that the Goodwillie derivatives can be refined to a lax functor $\\partial_* \\co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.20504/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}