{"id":"W4413965745","doi":"10.70930/tac/3zcjrcj6","title":"The category of extensions and idempotent completion","year":2024,"lang":"en","type":"article","venue":"Theory and applications of categories","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Norges Forskningsråd; Danmarks Grundforskningsfond; Trond Mohn stiftelse; Engineering and Physical Sciences Research Council; Aarhus Universitets Forskningsfond; London Mathematical Society; Aarhus Universitet; National Research Foundation; Alexander von Humboldt-Stiftung","keywords":"Idempotence; Mathematics; Computer science; Algebra over a field; Natural language processing; Pure mathematics","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":[0.001068999,0.0004267972,0.0003653764,0.001836196,0.001165624,0.00180836,0.0007466186,0.0005950644,0.003347384],"category_scores_gemma":[0.00140347,0.0002189628,0.0005835206,0.0007507176,0.003646728,0.006032442,0.003753907,0.001206822,0.0004939128],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006979905,"about_ca_system_score_gemma":0.0004933947,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005280773,"about_ca_topic_score_gemma":0.0003508406,"domain_scores_codex":[0.9990977,0.0001972183,0.00005297723,0.000218943,0.0002934031,0.0001397935],"domain_scores_gemma":[0.999043,0.0002841186,0.0001009477,0.0001309106,0.0002222415,0.0002186282],"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":[0.00003297163,0.00002952324,0.0008781905,0.00006005224,0.0000124473,0.0002475532,0.0009017166,0.0007970777,0.002389012,0.9833398,0.0004491207,0.01086245],"study_design_scores_gemma":[0.0000108988,0.00006694692,0.002208457,0.0000272354,0.00001119587,0.0006153064,0.0004516621,0.002827528,0.002573251,0.9722689,0.01891771,0.00002081381],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6132296,0.003087676,0.2797934,0.0009222277,0.0002512283,0.00007867522,0.0003694771,0.000276634,0.1019911],"genre_scores_gemma":[0.9558759,0.0007336481,0.0275676,0.0002211443,0.0001922791,0.00005981341,0.0003762194,0.00005667471,0.01491688],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003347384,"threshold_uncertainty_score":0.01119816,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.018854536098686,"score_gpt":0.3005861856080998,"score_spread":0.2817316495094138,"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."}}