The Category of Sets and Constructing Combinatorial Data Structures.
Abstract: Set theory is the foundation of modern mathematics, but the commonly used foundations are poorly suited for the everyday reasoning of mathematicians. They are also poorly suited for implementation in software. This talk will present an axiomatization of Set Theory due to Lawvere (1964) as updated by Leinster (2014) along with an application to the construction of combinatorial software. By getting the mathematics right, we can reduce complexity in the design of software systems. This material is a preview of a Fall 2021 special topics course on applied category theory CISE 4930: Abstraction, Composition, and Computation.
Fairbanks abstract^