{"id":"W3211462270","doi":"10.70930/tac/xclr43s4","title":"Pivotal objects in monoidal categories and their Hopf monads","year":2021,"lang":"en","type":"article","venue":"Theory and applications of categories","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Symmetric monoidal category; Enriched category; Dual (grammatical number); Mathematics; Closed monoidal category; Monoidal category; Construct (python library); Object (grammar); Pure mathematics; Discrete mathematics; 2-category; Cover (algebra); Combinatorics; Functor; Computer science; Linguistics; Programming language; Artificial intelligence","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000236755,0.0001402336,0.0002547518,0.00004910265,0.0001134984,0.0000324303,0.00009852795,0.00008019829,0.00002058923],"category_scores_gemma":[0.00008472161,0.0001158188,0.00003119044,0.0001952504,0.0002725408,0.00009525674,0.0001009676,0.0001072886,5.270029e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009228737,"about_ca_system_score_gemma":0.00006216048,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002351394,"about_ca_topic_score_gemma":0.00003037784,"domain_scores_codex":[0.9992786,0.00007619963,0.0002268564,0.0002058767,0.00007332348,0.0001391467],"domain_scores_gemma":[0.9990309,0.0004912107,0.00007928684,0.0002714088,0.00008009155,0.00004712535],"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":[0.00003627734,0.00004250349,0.0002590795,0.00007367569,0.00002048314,7.88107e-7,0.002808078,0.000001854196,0.0006442871,0.9925801,0.00001218934,0.003520732],"study_design_scores_gemma":[0.0002552818,0.00002162425,0.0004455704,0.000007013498,0.0000172513,0.00001426252,0.005840013,0.00001003843,0.01999703,0.9730141,0.0002584118,0.0001193928],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9891523,0.002487529,0.005603403,0.0001065537,0.00005450169,0.0002205666,0.00001076729,0.00003426063,0.002330159],"genre_scores_gemma":[0.9991204,0.0001732188,0.0002205863,0.0000226758,0.00006492798,0.0001036551,0.000007935934,0.00001351521,0.0002730704],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01956594,"threshold_uncertainty_score":0.4722955,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01081329438544769,"score_gpt":0.2519555655472782,"score_spread":0.2411422711618305,"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."}}