Timeline for Why is there a duality between spaces and commutative algebras?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2016 at 18:20 | comment | added | Qiaochu Yuan | Tim Campion's suggestion is that under mild hypotheses, categories of commutative algebras are coextensive, so their opposites are extensive. Extensivity is a categorical property that basically ensures that coproducts behave the way coproducts of spaces ought to (that they are really "disjoint" in a particular sense), so it's a reasonable candidate for a necessary condition a category should satisfy to be considered a category of "spaces." | |
| Sep 12, 2016 at 18:18 | comment | added | HeinrichD | Do you have an answer for this? To be honest, I didn't understand the other answers (and their relation to the question). | |
| Sep 12, 2016 at 17:39 | comment | added | Qiaochu Yuan | Sure, but why should these objects exist, and why should they relate things that look like spaces and things that look like commutative algebras? | |
| Sep 12, 2016 at 16:50 | history | answered | HeinrichD | CC BY-SA 3.0 |