{"paper":{"title":"The homotopy groups of the simplicial mapping space between algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Emanuel Rodr\\'iguez Cirone","submitted_at":"2018-03-21T18:45:08Z","abstract_excerpt":"Let $\\ell$ be a commutative ring with unit. To every pair of $\\ell$-algebras $A$ and $B$ one can associate a simplicial set $\\hom(A,B^\\Delta)$ so that $\\pi_0\\hom(A,B^\\Delta)$ equals the set of polynomial homotopy classes of morphisms from $A$ to $B$. We prove that $\\pi_n\\hom(A,B^\\Delta)$ is the set of homotopy classes of morphisms from $A$ to $B^{S_n}$, where $B^{S_n}$ is the ind-algebra of polynomials on the $n$-dimensional cube with coefficients in $B$ vanishing at the boundary of the cube. This is a generalization to arbitrary dimensions of a theorem of Corti\\~nas-Thom, which addresses the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08087","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"}