Timeline for When is the opposite of the category of algebras of a Lawvere theory extensive?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2022 at 12:45 | comment | added | Zhen Lin | You are welcome to state and prove a theorem for many-sorted algebraic theories if you like. | |
| Jan 1, 2022 at 12:35 | comment | added | Paul Taylor | One-sorted algebraic theories were a gratuitous handicap of the mid 20th century akin to the unit fractions of the ancient Egyptians. | |
| Jan 1, 2022 at 1:22 | comment | added | Zhen Lin | This argument is for one-sorted algebraic theories. I don't think it would be appropriate to introduce a new sort here. | |
| Dec 31, 2021 at 20:01 | comment | added | Paul Taylor | The tuples never break ranks, so you should have $\kappa=1$ by adding types and terms with equations to make them products, projections and pairings. I'm just being a categorist tidying up the mess of universal algebra. Maybe there is a purely categorical theorem of when there's a dual adjunction between (l)extensive categories. No disrespect to Broodryk, but I smell an idea that needs more than one insight, just as the double pullback formulation of extensivity did. | |
| Dec 31, 2021 at 18:12 | history | edited | Zhen Lin | CC BY-SA 4.0 |
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| Dec 31, 2021 at 18:09 | comment | added | Zhen Lin | It is not possible to have $\kappa = 0$ and also have a non-trivial theory. I think there is an ad hoc argument that shows that $\kappa = 1$ is impossible for the theory of commutative rigs. | |
| Dec 31, 2021 at 15:14 | comment | added | Paul Taylor | Thank for explaining that. Can you get rid of the $\kappa$-tuples? | |
| Dec 29, 2021 at 7:39 | history | edited | Zhen Lin | CC BY-SA 4.0 |
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| Dec 29, 2021 at 1:59 | history | answered | Zhen Lin | CC BY-SA 4.0 |