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Title:A theory of elementary higher toposes
Author(s):Rasekh, Nima
Director of Research:Rezk, Charles
Doctoral Committee Chair(s):Ando, Matthew
Doctoral Committee Member(s):McCarthy, Randy; Berwick-Evans, Dan
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Homotopy Theory Higher Category Theory Topos Theory
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.
Issue Date:2018-06-29
Type:Thesis
URI:http://hdl.handle.net/2142/101508
Rights Information:Copyright 2018 Nima Rasekh
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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