Timeline for What is the definition of "canonical"?
Current License: CC BY-SA 2.5
13 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jun 4, 2012 at 20:29 | comment | added | David Corwin | See the answer referring to page vii of the Introduction to the 1996 edition of Sheaf Theory by Glen E. Bredon for a comment relating to your rule of thumb. | |
| Apr 5, 2010 at 20:10 | comment | added | AndrewLMarshall | apologies, I read it wrong. | |
| Mar 28, 2010 at 20:34 | comment | added | Reid Barton | Sure, for example, the natural isomorphism $V \to V^{**}$ given by $x \mapsto (f \mapsto 3f(x))$. | |
| Mar 28, 2010 at 20:28 | comment | added | Dmitri Pavlov | >but the converse need not hold. Could you please give an example for this statement? | |
| Mar 28, 2010 at 20:15 | comment | added | François G. Dorais | @Reid: Returning to the question you asked me, I don't think I'm very comfortable writing "Hom(Z[x],R) = R." | |
| Mar 28, 2010 at 20:13 | comment | added | François G. Dorais | +1 for the rule of thumb. I think this is a very good litmus test. | |
| Mar 28, 2010 at 20:07 | history | edited | Reid Barton | CC BY-SA 2.5 |
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| Mar 28, 2010 at 19:52 | history | edited | Reid Barton | CC BY-SA 2.5 |
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| Mar 28, 2010 at 19:49 | comment | added | David Jordan | I think a correct precise definition would be a refinement of Reid's answer #1. There should be a unique isomorphism between any other candidate Y to the "canonical" X. As Reid mentions, this will require listing precisely the amount of information to yield only one isomorphism. | |
| Mar 28, 2010 at 18:46 | comment | added | Reid Barton | The OP asked for an incorrect use of the word "canonical", which I took to mean a false statement which becomes true if "canonical" is removed. | |
| Mar 28, 2010 at 18:45 | comment | added | AndrewLMarshall | 3. bothers me. Don't you want it to say "...and the dual of the dual," so the statement is correct? | |
| Mar 28, 2010 at 18:36 | history | answered | Reid Barton | CC BY-SA 2.5 |