{"paper":{"title":"Taxotopy Theory of Posets I: van Kampen Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Amit Kuber, David Wilding","submitted_at":"2015-10-29T21:55:37Z","abstract_excerpt":"Given functors $F,G:\\mathcal C\\to\\mathcal D$ between small categories, when is it possible to say that $F$ can be \"continuously deformed\" into $G$ in a manner that is not necessarily reversible? In an attempt to answer this question in purely category-theoretic language, we use adjunctions to define a `taxotopy' preorder $\\preceq$ on the set of functors $\\mathcal C\\to\\mathcal D$, and combine this data into a `fundamental poset' $(\\Lambda(\\mathcal C,\\mathcal D),\\preceq)$.\n  The main objects of study in this paper are the fundamental posets $\\Lambda(\\mathbf 1,P)$ and $\\Lambda(\\mathbb Z,P)$ for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08921","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"}