{"paper":{"title":"Unified Functorial Signal Representation III: Foundations, Redundancy, $L^0$ and $L^2$ functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CT","math.IT"],"primary_cat":"eess.SP","authors_text":"Salil Samant, Shiv Dutt Joshi","submitted_at":"2017-10-27T16:23:11Z","abstract_excerpt":"In this paper we propose and lay the foundations of a functorial framework for representing signals. By incorporating additional category-theoretic relative and generative perspective alongside the classic set-theoretic measure theory the fundamental concepts of redundancy, compression are formulated in a novel authentic arrow-theoretic way. The existing classic framework representing a signal as a vector of appropriate linear space is shown as a special case of the proposed framework.\n  Next in the context of signal-spaces as a categories we study the various covariant and contravariant forms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10227","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"}