{"paper":{"title":"Goodwillie Calculus via Adjunction and LS Cocategory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Rosona Eldred","submitted_at":"2012-09-11T18:01:09Z","abstract_excerpt":"In this paper, we show that for reduced homotopy endofunctors of spaces, F, and for all $n \\geq 1$ there are adjoint functors $R_n, L_n$ with $T_n F \\simeq R_n F L_n$, where $P_n F$ is the $n$-excisive approximation to $F$, constructed by taking the homotopy colimit over iterations of $T_n F$. This then endows $T_n$ of the identity with the structure of a monad and the $T_n F$'s are the functor version of bimodules over that monad. It follows that each $T_n F$ (and $P_nF$) takes values in spaces of symmetric Lusternik-Schnirelman cocategory $n$, as defined by Hopkins. This also recovers recent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2384","kind":"arxiv","version":4},"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"}