My Honours thesis was on Cohomology and Zappa–Szép products. In short we defined Zappa–Szép products of internal monoids of monoidal categories. Traditionally, there are two ways to define Zappa–Szép products: either through distributive laws or matched pairs of actions. We show that the definition of Zappa–Szép products in terms of distributive laws makes sense in any monoidal category, while the definition in terms of matched pairs only makes sense in cartesian monoidal categories. In cartesian monoidal categories the definitions are equivalent. We then unpack the work done on monadic homology done by Barr and Beck in the 70s and build a double complex which we conjecture can be used to compute the homology of Zappa–Szép products. The project was supervised by Alex Mundey and Aidan Sims.
Research Interests
Categorical Logic,
Type Theory,
Topos Theory,
Ordinal Analysis, and
Proof Assistants
Talks
The following are talks I have given (ordered in roughly reverse chronological order):
Cohomology and Zappa–Szép Products, UoW Honours Major Presentation
Equality in Elementary Fibrations, Australian Category Seminar
The Groupoid Interpretation of Equality, Wollongong OANCG Seminar
Building mathematical universes with category theory, AMSI Summer Research Project Presentation
How Many Holes does Isaac Have: Computing my Homology, UoW Undergraduate Project Presentation
A Brief Introduction to Nonclassical Logic, UOW Undergraduate Seminar
Lawvere's Fixed Point Theorem, UOW Undergraduate Seminar
Free and Forgetful Functors, UOW Undergraduate Seminar
Hutchinson's Theorem (together with Adam McCarthy, Elliot Mabbutt, Naomi Reed, Umar Babu, Olive Wunderwald, and Luke Kenshall) UOW Winter Scholars