A theory of elementary higher toposes

Homotopy TheoryHigher Category TheoryTopos Theory

Rasekh, Nima

关键词: Homotopy TheoryHigher Category TheoryTopos Theory;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101508/RASEKH-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.