Australian Category Seminar

In the category of sets and partial functions, the Cartesian product × is not a categorical product. Instead the categorical product is given by 𝐴 + 𝐵 + 𝐴 × 𝐵, where + is the disjoint union. In this talk, we give a restriction category explanation of why this is the case. We will show that in a distributive restriction category, 𝐴 + 𝐵 + 𝐴 × 𝐵 is a product if and only if the restriction category is classical, that is, has joins and relative complements.

This is joint work with Robin Cockett, based on our paper: (link) This will be an extended version of my talk at FMCS2023: (link) This will be a slide talk. FMCS slides are here: (link)