{"paper":{"title":"Unified Functorial Signal Representation I: From Grothendieck fibration to Base structured categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Salil Samant, Shiv Dutt Joshi","submitted_at":"2016-10-19T09:19:57Z","abstract_excerpt":"In this paper we study categories $(F,\\mathbf{C},\\mathbf{D})$ and $(\\mathbb{F},\\mathbf{C},\\mathbf{Set})$ and prove them to be fibred on $\\mathbf{C}$. Then we examine Grothendieck construction in the context of an ordinary functor $F: \\mathbf{C} \\rightarrow \\mathbf{D}$ through the concept of trivial categorification, using an appropriate functor $\\mathbf{F}: \\mathbf{C} \\xrightarrow{F} \\mathbf{D} \\xrightarrow{I} \\mathbf{Cat}$ to construct $\\int_{\\mathbf{C}^{op}} \\bar{\\mathbf{F}}$. This category characterizes a functor as an abstract right category action while its dual $\\mathcal{X} \\rtimes_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05926","kind":"arxiv","version":4},"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"}