Timeline for Symmetric monoidal functors from powers of the natural numbers to Set
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2023 at 17:11 | history | edited | Charles Wang |
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| Oct 9, 2023 at 17:09 | answer | added | Charles Wang | timeline score: 2 | |
| Oct 8, 2023 at 9:46 | answer | added | Martin Brandenburg | timeline score: 2 | |
| Oct 8, 2023 at 7:47 | comment | added | Maxime Ramzi | When the source and target are cartesian-monoidal, symmetric monoidal functors and product-preserving functors form equivalent categories | |
| Oct 8, 2023 at 3:46 | comment | added | Qiaochu Yuan | (These are a priori different; for a functor $F : C \to D$ to be product-preserving means that the canonical map $F(X \times Y) \to F(X) \times F(Y)$, which exists because of the universal property of the product, is an isomorphism. In particular this is a property of a functor $F$. Whereas being a symmetric monoidal functor only requires some coherent collection of such isomorphisms to exist, not necessarily the canonical one, and is extra structure on a functor $F$ in general. This distinction is probably why Tim asked what symmetric monoidal structures you were taking.) | |
| Oct 8, 2023 at 3:44 | comment | added | Qiaochu Yuan | @Charles: FWIW I think it would have been a lot less confusing to talk about the powers of $\mathbb{N}$ as a Lawvere theory (this makes it clear that $\mathbb{N}$, at least, is a model of this theory, which is otherwise not so obvious). It would also perhaps be useful context to note in the text of the question that if $\mathbb{N}$ is replaced with $\{ 0, 1 \}$ the resulting Lawvere theory is the Lawvere theory of Boolean algebras. Also, do you really mean "symmetric monoidal functors" or do you mean product-preserving functors in the usual Lawvere theory way? | |
| Oct 8, 2023 at 0:51 | history | edited | Martin Brandenburg | CC BY-SA 4.0 |
added 9 characters in body
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| Oct 4, 2023 at 2:25 | comment | added | Charles Wang | I'm only looking at 1 and the infinite countable sets. The 'actual' category is the full subcategory containing 1 and the powers of the natural numbers, but this is identical to the category stated. | |
| Oct 1, 2023 at 20:10 | comment | added | Martin Brandenburg | I am confused by the definition. It sounds as if 1 is not countable, but it is. You are considering the category of all countable sets right? Or do you only look at 1 and the infinite ones? | |
| Sep 28, 2023 at 14:34 | comment | added | Charles Wang | Yes, I'm taking the Cartesian monoidal structure here. | |
| Sep 28, 2023 at 8:51 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Sep 28, 2023 at 3:34 | comment | added | Alec Rhea | @TimCampion Wouldn’t Cartesian products be the canonical choice? | |
| Sep 28, 2023 at 1:37 | comment | added | Tim Campion | Which symmetric monoidal structures are you taking on these categories? | |
| Sep 28, 2023 at 0:45 | history | asked | Charles Wang | CC BY-SA 4.0 |