{"id":"W2127640939","doi":"10.70930/tac/ej5u1k5p","title":"An embedding theorem for Hilbert categories","year":2009,"lang":"en","type":"article","venue":"Theory and applications of categories","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":38,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Embedding; Axiom; Pure mathematics; Morphism; Functor; Hilbert space; Hilbert manifold; Symmetric monoidal category; Enriched category; Hilbert R-tree; Monoidal category; Closed monoidal category; Hilbert's basis theorem; Algebra over a field; Rigged Hilbert space; Reproducing kernel Hilbert space; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001610659,0.0004234433,0.0003843851,0.001343189,0.001106484,0.001928471,0.0006975091,0.0008325835,0.006345869],"category_scores_gemma":[0.002366957,0.0002729237,0.0007871434,0.0007292688,0.003235186,0.007128296,0.00355084,0.00183709,0.0009164765],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009829346,"about_ca_system_score_gemma":0.0005182602,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005844209,"about_ca_topic_score_gemma":0.0004107924,"domain_scores_codex":[0.9989539,0.0002828106,0.00007333804,0.0002351367,0.0003103222,0.0001444283],"domain_scores_gemma":[0.9986237,0.0006013804,0.00008513687,0.0002087845,0.0003502068,0.0001308112],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000003829982,0.000005942139,0.0001351763,0.00002484932,0.000005093353,0.0000358459,0.0002692861,0.000195377,0.0005715761,0.9921216,0.0007418064,0.005889684],"study_design_scores_gemma":[0.000006678668,0.00002425234,0.0003251791,0.00001727428,0.00000647178,0.0002098893,0.00012221,0.001954448,0.0009509432,0.9689872,0.02738515,0.00001040086],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07962919,0.00305166,0.7854446,0.003233171,0.0005830165,0.00008479974,0.0004747106,0.0006618519,0.126837],"genre_scores_gemma":[0.8336393,0.001194413,0.1376286,0.001171458,0.0005149657,0.0001806374,0.0005538642,0.0002064625,0.0249104],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006345869,"threshold_uncertainty_score":0,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01556039060464528,"score_gpt":0.3193703177223238,"score_spread":0.3038099271176785,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}