{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101508"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101508","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A theory of elementary higher toposes","abstract":"The end goal of this work is to define and study an elementary higher topos. We will achieve this by going through several steps. First we review complete Segal spaces. Then we study various fibrations of complete Segal spaces and use that to define representable Cartesian fibrations. Next we use representable Cartesian fibrations to define complete Segal objects which are are model for internal higher categories. Having done all this work we can then define an elementary higher topos which simultaneously generalizes an elementary topos and higher topos. Then we use all the tools we previously developed to show it satisfies classical topos theoretic properties, such being locally Cartesian closed and descent. Finally we show we can classify univalent maps in an elementary higher topos.","abstract_html":"The end goal of this work is to define and study an elementary higher topos. We will achieve this by going through several steps. First we review complete Segal spaces. Then we study various fibrations of complete Segal spaces and use that to define representable Cartesian fibrations. Next we use representable Cartesian fibrations to define complete Segal objects which are are model for internal higher categories. Having done all this work we can then define an elementary higher topos which simultaneously generalizes an elementary topos and higher topos. Then we use all the tools we previously developed to show it satisfies classical topos theoretic properties, such being locally Cartesian closed and descent. Finally we show we can classify univalent maps in an elementary higher topos.","abstract_has_math":false,"creators":["Rasekh, Nima"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles","Ando, Matthew","McCarthy, Randy","Berwick-Evans, Dan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:33Z","date_published":"2018-09-27T16:17:33Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Homotopy Theory Higher Category Theory Topos Theory"],"languages":["en"],"rights":["Copyright 2018 Nima Rasekh"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101508","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles","Ando, Matthew","McCarthy, Randy","Berwick-Evans, Dan"]},{"key":"dc:creator","label":"Author","values":["Rasekh, Nima"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:33Z","2018-06-29","2018-08"]},{"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":["Homotopy Theory Higher Category Theory Topos Theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Nima Rasekh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101508"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The end goal of this work is to define and study an elementary higher topos. We will achieve this by going through several steps. First we review complete Segal spaces. Then we study various fibrations of complete Segal spaces and use that to define representable Cartesian fibrations. Next we use representable Cartesian fibrations to define complete Segal objects which are are model for internal higher categories. Having done all this work we can then define an elementary higher topos which simultaneously generalizes an elementary topos and higher topos. Then we use all the tools we previously developed to show it satisfies classical topos theoretic properties, such being locally Cartesian closed and descent. Finally we show we can classify univalent maps in an elementary higher topos.","Submission original under an indefinite embargo labeled 'Open Access'. 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Then we study various fibrations of complete Segal spaces and use that to define representable Cartesian fibrations. Next we use representable Cartesian fibrations to define complete Segal objects which are are model for internal higher categories. Having done all this work we can then define an elementary higher topos which simultaneously generalizes an elementary topos and higher topos. Then we use all the tools we previously developed to show it satisfies classical topos theoretic properties, such being locally Cartesian closed and descent. Finally we show we can classify univalent maps in an elementary higher topos.","Submission original under an indefinite embargo labeled 'Open Access'. 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