Watch my most recent talk!
Partial functions and other generalised coproduct completions
1st September 2026
The category of sets and functions is the free coproduct completion of the terminal category. In a double-categorical setting, Evan Patterson defined a new notion of double (co)product and used it to prove that the double category of sets, functions and spans is the free coproduct completion of the terminal double category. In this talk we both generalise and refine this notion. First, we extend Patterson’s original definition to include (co)products in (co)virtual double categories, which can capture examples such as coproducts in Span(C) even when C does not have pullbacks. Second, we isolate finer classes of double (co)products, denoted (L,R)-(co)products, where L and R are certain classes of functions. As an application, we exhibit the double category of sets, functions and partial functions as a free (L,R)-coproduct completion of the terminal double category.
Hello,
I'm a mathematician and PhD candidate at Case Western Reserve University. This summer I was also RA at topos institute. I'm interested in exploring ideas in double category theory. In particular, I want to understand notions of presentable double categories, compact closed double categories and their use in answering questions in category theory and other areas of mathematics.
Recently, I have also been learning how to apply formal methods of category theory to real world problems.
Beyond this, I am drawn to all ideas that explore the search for truth and the beauty it reveals.
On this website, you'll find:
- About me: A description of my given talks, papers and events I helped organize.
- Conversations with friends: I like thinking about things and having long conversations with others about things. In this section I want to keep a record of some of the things thought and conversated.
If you find something here that resonates with you, you want to collaborate on a project or just want to say hello; feel free to reach out to me at axh1127@case.edu.