The geometry of sheaves on sites
Date
2021-01
Authors
Editor(s)
Advisor
Ünlü, Özgün
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Print ISSN
Electronic ISSN
Publisher
Bilkent University
Volume
Issue
Pages
Language
English
Type
Thesis
Journal Title
Journal ISSN
Volume Title
Series
Abstract
In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we introduce the notion of varieties, and show the relationship between certain class of varieties known as diffeologies with the category of smooth manifolds. Along the way, the notion of schemes will be generalized as a variety on symmetric monoidal categories. And we show how a differential geometric construction on a site can be translated to a construction on generalized spaces.