Fall 2024

MATH 6710, T Th 1:45 - 3:15 p.m., DRL 4E9

Topics in Logic: Category Theory, Categorical Logic, and Type Theory

Professor Andre Scedrov

Prerequisites

Some Suggested References

• Samson Abramsky and Nikos Tzevelekos: "Introduction to Categories and Categorical Logic", 2011.
• Egbert Rijke: "Introduction to Homotopy Type Theory". Part I, Martin-Löf's Dependent Type Theory, 2022, pp. i-xiii, 1-97.
• Saunders Mac Lane: "Categories for the Working Mathematician". Graduate Texts in Mathematics, volume 5, Springer New York, NY, Second Edition, Paperback, 2010. ISBN: 978-1-4419-3123-8.
• Michael Barr and Charles Wells: "Category Theory for Computing Science", Revised, 2020.
• Joachim Lambek and Philip J. Scott: "Introduction to Higher-Order Categorical Logic". Cambridge Studies in Advanced Mathematics, Series Number 7, 1988. ISBN: 9780521356534.
• Saunders Mac Lane and Ieke Moerdijk: "Sheaves in Geometry and Logic", Universitext, Springer New York, NY. eBook ISBN 978-1-4612-0927-0, Published: 06 December 2012.
• Peter T. Johnstone: "Topos Theory", Dover, 18th December 2013. Reprint of the Academic Press, New York, 1977 edition. ISBN: 9780486493367.
• Peter J. Freyd and Andre Scedrov: "Categories, Allegories", Elsevier, 1990. eBook ISBN: 9780080887012.

Basic Course Information

Please think which papers and/or book chapters or sections you would like to present in class during the fall semester and let me know. We will have an organizational meeting the first day of classes on Tuesday, August 27, 2024. Ideally, we would have a presentation lined up ready to start at the following class on Thursday, August 29, 2024.

Please plan on including in your presentations a generous amount of background material and please pitch the presentations appropriately for the students who might not have taken Math 5710 in Spring 2024, but who are interested in taking Math 6710 in Fall 2024 nevertheless.