Joe MoellerSep 17, 2024

Neither “Categorical product” nor “Cartesian product” are ideal descriptors imo. How are tensor products or coproducts not categorical? Cartesian is confusing when the product is not given by pairs, or when pairs gives a different monoidal structure.

I’m not sure why nobody afaict has used “limit product”.

Show threadazul
@Joemoeller yes! i wrote about this on here some time ago, the exact same issue that "cartesian product" is not a good description for that limit in an arbitrary category. "limit product" is nice. in my thread i proposed "projection product" because it is defined by its projection morphisms.
Sep 18, 2024 at 2:48pmWeb
Show threadazulSep 18, 2024
@Joemoeller oh this is all i wrote, i think ... https://gamedev.lgbt/@typeswitch/112898260454632466
lawless polymorph (@[email protected])

@[email protected] ok i don't actually hate cartesian product and CCCs, but i do have two issues: 1. cartesian closed categories are not that common in computing, or in general. 2. tuples being the main way of working with the original cartesian product ... the generalization of the cartesian product from Set to other categories, *should have been the tensor product*, not the (limit definition via projections) "product".

🏳️‍🌈 Gamedev ❤️ LGBTQIA+
Show threadZanzi @ Monoidal CafeSep 18, 2024
@typeswitch @Joemoeller I tend to use "cartesian product" just because the average programmer tends to
know just a couple of basic limits/colimits rather than limits in general. so it keeps my writing more accessible. 🙃