{"paper":{"title":"Dendroidal Sets","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Ieke Moerdijk, Ittay Weiss","submitted_at":"2007-01-10T15:19:32Z","abstract_excerpt":"We introduce the concept of a dendroidal set. This is a generalization of the notion of a simplicial set, specially suited to the study of operads in the context of homotopy theory. We define a category of trees, which extends the category $\\Delta$ used in simplicial sets, whose presheaf category is the category of dendroidal sets. We show that there is a closed monoidal structure on dendroidal sets which is closely related to the Boardman-Vogt tensor product of operads. Furthermore we show that each operad in a suitable model category has a coherent homotopy nerve which is a dendroidal set, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701293","kind":"arxiv","version":2},"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"}