Timeline for What is a reference for profinite sets?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2011 at 23:10 | comment | added | Gonçalo Marques | Another reference is "Algèbre et Théories galoisiennes" by Régine et Adrien Douady namely pag. 63-64 | |
| Mar 3, 2010 at 16:34 | comment | added | Pete L. Clark | Thanks, Marty. This sounds like a good definition to me. (Indeed, the Stone-Cech compactification of a discrete space is totally disconnected...i.e., a Stone space!) | |
| Mar 3, 2010 at 6:03 | comment | added | jackie boy | What I am calling the profinite completion of a set is almost the same as for a group, except everytime the word group is used, you replace it the with the word set. Now the Stone Cech compactifaication of a (discrete) space misses the words, "totally disconnected". Wikipedia states (so a grain of salt) that the stone cech compactification happens to be totally disconnected. So ths notion of profinite completion seems to be the stone cech compactification. I would like to make a remark on the terminology. Any concrete category with filtered limits has a "profinite completion" functor. | |
| Mar 3, 2010 at 4:11 | comment | added | Marty | Excuse my high brows :) I didn't say anything about profinite completions -- I don't know a definition of "the profinite completion of a set". Given a set $X$, endowed with the discrete topology, perhaps the Stone-Cech compactification $\beta X$ satisfies an appropriate universal property to be called a "profinite completion of $X$". I wouldn't use this terminology though! "Profinite completion" should only be used for groups, I think. | |
| Mar 3, 2010 at 2:34 | comment | added | Pete L. Clark | This is a little highbrow for my taste. [Marty is an old friend of mine, so I know he can take being called "highbrow" with a smile.] Suppose that $S$ is a countably infinite set. Its profinite completion is...? | |
| Mar 2, 2010 at 23:54 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 23:53 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 23:53 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 22:33 | comment | added | Marty | Whoops - I forgot about the Yoneda reversal. I think it's correct now. Thanks Leonid! | |
| Mar 2, 2010 at 22:32 | history | edited | Marty | CC BY-SA 2.5 |
Fixed a small error.
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| Mar 2, 2010 at 22:27 | comment | added | Leonid Positselski | More precisely, objects of $Pro(Set_f)$ are covariant functors from $Set_f$ to $Set$ which are filtered inductive (rather than projective) limits of representable functors. | |
| Mar 2, 2010 at 22:11 | history | answered | Marty | CC BY-SA 2.5 |