Timeline for Subtle distinction in "completeness"?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2022 at 15:36 | comment | added | Yemon Choi | Counterargument for someone who does like categorical thinking in functional analysis (as you know) - when doing any actual harmonic analysis on locally compact groups $C_c(G)$ is incredibly useful as a convolution algebra, both for building general theory and for doing actual calculations / 3-epsilon arguments ... | |
| Aug 29, 2022 at 17:39 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
added 40 characters in body
|
| Aug 29, 2022 at 17:39 | comment | added | Qiaochu Yuan | I was thinking about mentioning that but it's not relevant to this discussion because it's contravariant anyway. We're looking for a covariant functor in this setting. | |
| Aug 29, 2022 at 13:10 | comment | added | terceira | Just a modest comment on the last paragraph. I don't think that the phrase " not functorial at all" is very helpful or even correct. This assignment IS functorial on the class of locally compact spaces, but with the proper mappings rather than the continuous ones as morphisms. This is, of course, just a semi-category rather than a category but that doesn't mean that it is not a useful circle of ideas. Another context where it is appropriate is the extension of Gelfand duality to one between locally compact spaces and commutative $C^\ast$-algebras. | |
| Aug 29, 2022 at 1:52 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |