Doctrines are a category-theoretic reformulation of the concept of a theory from mathematical logic. In this project we will focus on the use of doctrines to present fragments of first order logic. Some doctrines have a notion of equality. Work by Fabio Pasquali has shown that doctrines that present first order logic can freely be given a notion of equality. This project seeks to generalise this result from doctrines to fibrations.
University of Wollongong
Isaac is a third-year student at University of Wollongong, studying the Bachelor of Mathematics, majoring in pure maths. Isaac’s research interests primarily in the connection between geometry and logic, and the use of category theory to study this. He is also interested in automated theorem proving, program synthesis, and how categories can be applied to these problems. Isaac is the founder and organiser of the UOW undergraduate seminar and the current president of the UOW Mathematics and Statistics Society. Outside of Mathematics Isaac enjoys hiking, camping, and gymnastics.