{"paper":{"title":"Standard $t$-structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Jean-Baptiste Teyssier, Mauro Porta, Peter J. Haine","submitted_at":"2025-04-10T05:55:43Z","abstract_excerpt":"We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\\infty$-categories of sheaves. More precisely, given a presentable $\\infty$-category $\\mathcal{X}$ and a presentable stable $\\infty$-category $\\mathcal{E}$ equipped with an accessible $t$-structure $\\tau = (\\mathcal{E}_{\\geq 0}, \\mathcal{E}_{\\leq 0})$, we show that $\\mathcal{X} \\otimes \\mathcal{E}$ is equipped with a canonical $t$-structure whose coconnective part is given in $\\mathcal{X} \\otimes \\mathcal{E}_{\\leq 0}$. When $\\mathcal{X}$ is an $\\infty$-topos, we give a more explicit descr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.07473/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"}