Timeline for Why it is convenient to be cartesian closed for a category of spaces?
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11 events
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| Sep 12, 2021 at 21:16 | comment | added | Paul Taylor | Some of the comments on this question are also relevant. | |
| Sep 12, 2021 at 12:16 | answer | added | Tim Campion | timeline score: 1 | |
| Sep 12, 2021 at 11:51 | answer | added | Tim Campion | timeline score: 6 | |
| Sep 12, 2021 at 10:51 | comment | added | Alexander Schmeding | Just wanted to point out that cartesian closedness is also the selling point of convenient calculus (See The convenient setting of global Analysis by Kriegl/Michor whose title is based on Steenrods Paper but ironically leads to a category of smooth maps which May be discontinuous.) In Differential geometry the Appeal og cartesian closedness is that you can play back the question of differentiability of a map into the Homset to differentiability on a product which is usually much easier to Check. | |
| Sep 12, 2021 at 2:03 | history | became hot network question | |||
| Sep 11, 2021 at 23:47 | answer | added | Gregory Arone | timeline score: 11 | |
| Sep 11, 2021 at 20:47 | comment | added | Simon Henry | I have no reference that would explain what Steenrod had in mind exactly, but I think it's just that we want to be able to study the homotopy typeof the space of maps $X \to Y$ for $X$ and $Y$ two spaces. In more modern terminology, the $\infty$-category of "spaces" is cartesian closed, so we want to present it by a cartesian closed model category. | |
| Sep 11, 2021 at 18:43 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Sep 11, 2021 at 18:16 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Sep 11, 2021 at 18:06 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Sep 11, 2021 at 17:57 | history | asked | Ivan Di Liberti | CC BY-SA 4.0 |