Algebra in a localic topos with applications to ring theory

Applications of geometric logic to topos approaches to quantum theory

This document describes my 3-year project “Applications of geometric logic to topos approaches to quantum theory”, to start in 2009 with funding from the UK Engineering and Physical Sciences Research Council (EPSRC) for a post-doctoral Research Assistant and a PhD studentship. After an overview of the background and programme of work, it leads on to a description of the high-grade postdoctoral ...

An Introduction to Topos Theory

The purpose of this text is to equip the reader with an intuitive but precise understanding of elementary structures of category and topos theory. In order to achieve this goal, we provide a guided tour through category theory, leading to the definition of an elementary (Lawvere–Tierney) topos. Then we turn to the investigation of consequences of this definition. In particular, we analyse in de...

Localic Galois Theory

In this article we prove the following: A topos with a point is connected atomic if and only if it is the classifying topos of a localic group, and this group can be taken to be the locale of automorphisms of the point. We explain and give the necessary definitions to understand this statement. The hard direction in this equivalence was first proved in print in [4], Theorem 1, Section 3, Chapte...

Module theory over the exterior algebra with applications to combinatorics

Acknowledgements My deepest thanks go to Tim Römer for his guidance into mathematics and mathematical life since many years now, his support and encouragement during all that time. I wish to thank Winfried Bruns for his interest and many warm and refreshing conversations. I thank Christof and Jochen for always listening to my more or more often less exigent problems. I would also like to thank ...

Higher Topos Theory