Dissertations, Theses, and Capstone Projects

Date of Degree

6-2023

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

John Terilla

Committee Members

Thomas Tradler

Noson Yanofsky

Mahmoud Zeinalian

Subject Categories

Geometry and Topology | Other Mathematics

Keywords

sheaf, category theory, topology, topos

Abstract

This document details the body of theory necessary to explicitly construct sheaves of sets on a site together with the development of supporting material necessary to connect sheaf theory with the wider mathematical contexts in which it is applied. Of particular interest is a novel presentation of the plus construction suitable for direct application to a site without first passing to the generated grothendieck topology.

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