A theory of elementary higher toposes

Rasekh, Nima

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https://hdl.handle.net/2142/101508 Copy

Description

Title

A theory of elementary higher toposes

Author(s)

Rasekh, Nima

Issue Date

2018-06-29

Director of Research (if dissertation) or Advisor (if thesis)

Rezk, Charles

Doctoral Committee Chair(s)

Ando, Matthew

Committee Member(s)

• McCarthy, Randy
• Berwick-Evans, Dan

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Date of Ingest

2018-09-27T16:17:33Z

Keyword(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.

Graduation Semester

2018-08

Type of Resource

text

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

Copyright and License Information

Copyright 2018 Nima Rasekh

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