{"paper":{"title":"Parametrized K-Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.CT"],"primary_cat":"math.KT","authors_text":"Nicolas Michel","submitted_at":"2013-04-02T03:28:31Z","abstract_excerpt":"In nature, one observes that a K-theory of an object is defined in two steps. First a \"structured\" category is associated to the object. Second, a K-theory machine is applied to the latter category to produce an infinite loop space. We develop a general framework that deals with the first step of this process. The K-theory of an object is defined via a category of \"locally trivial\" objects with respect to a pretopology. We study conditions ensuring an exact structure on such categories. We also consider morphisms in K-theory that such contexts naturally provide. We end by defining various K-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0520","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"}