{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22388"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22388","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"State transformers and modes of computation","abstract":"State transformers, which form the objects in a subequalizing category, are a generalization of the transition functions of automata. The 2-categorical properties of subequalizers are developed and related to adjunctions in a 2-category. A calculus of monads in a 2-category is presented, and general lifting theorems are proved. Applications to constructions in categorical automata theory are given, and a representation theorem for strong monads into the monad of continuations is proved.","abstract_html":"State transformers, which form the objects in a subequalizing category, are a generalization of the transition functions of automata. The 2-categorical properties of subequalizers are developed and related to adjunctions in a 2-category. A calculus of monads in a 2-category is presented, and general lifting theorems are proved. Applications to constructions in categorical automata theory are given, and a representation theorem for strong monads into the monad of continuations is proved.","abstract_has_math":false,"creators":["Carpenter, Bruce Franklin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Gray, John"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:38:15Z","date_published":"2011-05-07T13:38:15Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Mathematics","Computer Science"],"languages":["eng"],"rights":["Copyright 1995 Carpenter, Bruce Franklin"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522087","(UMI)AAI9522087"],"render_values":[{"text":"AAI9522087","href":null,"code":true},{"text":"(UMI)AAI9522087","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22388","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Gray, John"]},{"key":"dc:creator","label":"Author","values":["Carpenter, Bruce Franklin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:38:15Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Carpenter, Bruce Franklin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522087","(UMI)AAI9522087","http://hdl.handle.net/2142/22388"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["State transformers, which form the objects in a subequalizing category, are a generalization of the transition functions of automata. The 2-categorical properties of subequalizers are developed and related to adjunctions in a 2-category. A calculus of monads in a 2-category is presented, and general lifting theorems are proved. Applications to constructions in categorical automata theory are given, and a representation theorem for strong monads into the monad of continuations is proved.","Made available in DSpace on 2011-05-07T13:38:15Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9522087.pdf: 3146338 bytes, checksum: 903d29655f5d7836a0c0a7feedfa5a05 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["State transformers and modes of computation"]}]}],"canonical_facts":{"dc:contributor":["Gray, John"],"dc:creator":["Carpenter, Bruce Franklin"],"dc:date":["2011-05-07T13:38:15Z","10000-01-01","1995"],"dc:description":["State transformers, which form the objects in a subequalizing category, are a generalization of the transition functions of automata. The 2-categorical properties of subequalizers are developed and related to adjunctions in a 2-category. A calculus of monads in a 2-category is presented, and general lifting theorems are proved. Applications to constructions in categorical automata theory are given, and a representation theorem for strong monads into the monad of continuations is proved.","Made available in DSpace on 2011-05-07T13:38:15Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9522087.pdf: 3146338 bytes, checksum: 903d29655f5d7836a0c0a7feedfa5a05 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9522087","(UMI)AAI9522087","http://hdl.handle.net/2142/22388"],"dc:language":["eng"],"dc:rights":["Copyright 1995 Carpenter, Bruce Franklin"],"dc:subject":["Mathematics","Computer Science"],"dc:title":["State transformers and modes of computation"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:19Z"}