{"paper":{"title":"Extension between functors from groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AT","authors_text":"Christine Vespa (IRMA)","submitted_at":"2015-11-10T13:18:39Z","abstract_excerpt":"Motivated in part by the study of the stable homology of automorphism groups of free groups, we consider cohomological calculations in the category $\\mathcal{F}(\\textbf{gr})$ of functors from finitely generated free groups to abelian groups.In particular, we compute the groups $Ext^*\\_{\\mathcal{F}(\\textbf{gr})}(T^n \\circ \\mathfrak{a}, T^m \\circ \\mathfrak{a})$ where $\\mathfrak{a}$ is the abelianization functor and $T^n$ is the n-th tensor power functor for abelian groups. These groups are shown to be non-zero if and only if $*=m-n \\geq 0$ and $Ext^{m-n}\\_{\\mathcal{F}(\\textbf{gr})}(T^n \\circ \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03098","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"}