A theory of elementary higher toposes

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Rasekh, Nima

Contributors dc:contributor

• Rezk, Charles
• Ando, Matthew
• McCarthy, Randy
• Berwick-Evans, Dan

• Homotopy Theory Higher Category Theory Topos Theory

Statement dc:rights

• Copyright 2018 Nima Rasekh

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101508

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101508