{"paper":{"title":"Gluing derived equivalences together","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Hideto Asashiba","submitted_at":"2012-04-01T11:01:22Z","abstract_excerpt":"The Grothendieck construction of a diagram $X$ of categories can be seen as a process to construct a single category $\\Gr(X)$ by gluing categories in the diagram together. Here we formulate diagrams of categories as colax functors from a small category $I$ to the 2-category $\\kCat$ of small $\\k$-categories for a fixed commutative ring $\\k$. In our previous paper we defined derived equivalences of those colax functors. Roughly speaking two colax functors $X, X' \\colon I \\to \\kCat$ are derived equivalent if there is a derived equivalence from $X(i)$ to $X'(i)$ for all objects $i$ in $I$ satisfyi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0196","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"}