## Classical distributive restriction categories

### JS Lemay – 13 September 2023

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: https://arxiv.org/abs/2305.16524
This will be an extended version of my talk at FMCS2023: https://www.reluctantm.com/gcruttw/fmcs2023/
This will be a slide talk. FMCS slides are here: https://www.reluctantm.com/gcruttw/fmcs2023/Slides/lemay.pdf

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