Timeline for Being (co)cartesian as a property (rather than structure) of a plain monoidal category
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4 at 18:12 | answer | added | varkor | timeline score: 4 | |
| Jan 27, 2021 at 20:47 | comment | added | Maxime Ramzi | For 1., aren't you satisfied with the naive proof ? That just takes a monoidal functor and shows that it preserves finite coproducts, and that in fact the structural morphisms are induced by the universal property of coproducts. I tried to think about 2. as well and reached the same conclusion, with the exact same condition (3) - I'm not sure how to remove it | |
| Jan 27, 2021 at 20:09 | comment | added | Tim Campion | @varkor Wow, that's a great point... somehow I went through that whole thing thinking as though I were in a symmetric monoidal setting, not really registering that symmetry was neither stipulated nor used! So I suppose that gives an answer! But yes, I do think it would be desireable to have a formulation based around monoid structures. The point of departure here is the description in terms of commutative monoid structures in the symmetric case, and the question of whether it's really necessary to assume symmetry / commutativity ("surely it should come for free via Eckmann-Hilton!") | |
| Jan 27, 2021 at 19:59 | comment | added | varkor | Isn't it the case that a suitable property is "$\otimes$ has a right adjoint", per your answer to Monoidal categories whose tensor has a left adjoint? Or do you explicitly want a property in the form "every object is a monoid [...]"? | |
| Jan 27, 2021 at 19:19 | history | asked | Tim Campion | CC BY-SA 4.0 |