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 threadBenjamin RogollSep 18, 2024
@Joemoeller i think personally we should call them groupoidal categories. And in this case they should it should be called a groupoidal product.
Show threadJoe MoellerSep 18, 2024
@JewleZi groupoidal category is a great name for a 2-category with all 2-cells being invertible, a category enriched in groupoids. I’m not even sure what Cartesian product has to do with groupoids.
Show threadBenjamin Rogoll
@Joemoeller no i meant cartesian monoidal categories actually. Since you can define groups in them, whereas in monoidal categories you can only define monoids
Sep 18, 2024 at 6:47amWeb
Show threadJoe MoellerSep 18, 2024
@JewleZi I know, I was explaining why I didn’t like that suggestion.