Timeline for Does the category of locally compact Hausdorff spaces with proper maps have products?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 8, 2023 at 16:15 | history | edited | YCor | CC BY-SA 4.0 |
made title more precise
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| Mar 8, 2023 at 14:44 | vote | accept | Oddly Asymmetric | ||
| Mar 8, 2023 at 14:30 | vote | accept | Oddly Asymmetric | ||
| Mar 8, 2023 at 14:31 | |||||
| Mar 8, 2023 at 13:42 | history | became hot network question | |||
| Mar 8, 2023 at 9:31 | answer | added | Tyrone | timeline score: 11 | |
| Mar 8, 2023 at 7:04 | comment | added | Emily | @OddlyAsymmetric Hmm, now that you mention it I'm not sure whether Tyrone means that the usual product space isn't the product in [LCHaus w/ proper maps] or if the projections failing to be proper somehow imply that [LCHaus w/ proper maps] doesn't have products. (I feel like it's probably the former, but the note says "products in [LCHaus w/ proper maps] don't exist", so again I'm not really sure...). Maybe you could try asking them if they could elaborate (Or hopefully they'll simply see this question :), I've seen Tyrone here (or on MSE?) before) | |
| Mar 8, 2023 at 6:33 | comment | added | Oddly Asymmetric | @Emily I'm not sure that is quite right, it seems to be suggesting that the product would be the same as that in Top, and of course that product doesn't work, but I'm asking if there is a different topological space which is the product in this category. Note that for example, colimits must be different in this category (i.e. the coproduct of locally compact Hausdorff spaces in Top won't be the coproduct in this category, since the *-compactification must preserve colimits into KHaus, and those are just disjoint unions) | |
| Mar 8, 2023 at 6:08 | comment | added | მამუკა ჯიბლაძე | Just want to note - whereas products in the category of topological spaces and local homeomorphisms are indeed weird (there is no terminal object in fact), pullbacks there are quite nice. | |
| Mar 8, 2023 at 5:53 | comment | added | Emily | Page 6 of Tyrone Cutler's note here says the product may fail to exist since the projections can fail to be proper (but also remarks that nevertheless at least $\times$ is part of a non-Cartesian monoidal structure on the category of locally compact Hausdorff spaces with proper maps) | |
| Mar 8, 2023 at 5:37 | history | asked | Oddly Asymmetric | CC BY-SA 4.0 |