2026-09-22T12:53:26Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/101508 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Rezk, Charles Ando, Matthew McCarthy, Randy Berwick-Evans, Dan Rasekh, Nima 2018-09-27T16:17:33Z 2018-09-27T16:17:33Z 2018-06-29 2018-08 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'. The submission was exported from vireo on 2018-09-27 without embargo terms The student, Nima Rasekh, accepted the attached license on 2018-06-28 at 00:37. The student, Nima Rasekh, submitted this Dissertation for approval on 2018-06-28 at 00:41. This Dissertation was approved for publication on 2018-06-29 at 09:06. DSpace SAF Submission Ingestion Package generated from Vireo submission #12678 on 2018-09-27 at 10:45:55 Made available in DSpace on 2018-09-27T16:17:33Z (GMT). No. of bitstreams: 4 RASEKH-DISSERTATION-2018.pdf: 1590520 bytes, checksum: 73a72c08b03da52762792660b1445aa1 (MD5) Thesis.zip: 4937282 bytes, checksum: 33f8bb08ad73d04970b782564be0753e (MD5) LICENSE.txt: 4208 bytes, checksum: 6cf656d55893a5eac7f206eceb165462 (MD5) PROQUEST_LICENSE.txt: 4554 bytes, checksum: f195ab6e9520289470922041638aebad (MD5) Previous issue date: 2018-06-29 application/pdf http://hdl.handle.net/2142/101508 en Copyright 2018 Nima Rasekh Homotopy Theory Higher Category Theory Topos Theory A theory of elementary higher toposes text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.