tea.mathoverflow.net - Discussion Feed (Some cleaned up comments) Sun, 04 Nov 2018 13:36:31 -0800 http://mathoverflow.tqft.net/ Lussumo Vanilla 1.1.9 & Feed Publisher darijgrinberg comments on "Some cleaned up comments" (19507) http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19507#Comment_19507 http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19507#Comment_19507 Sun, 08 Jul 2012 05:20:12 -0700 darijgrinberg Oops, my attention span needs some work.

]]> Joel Reyes Noche comments on "Some cleaned up comments" (19505) http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19505#Comment_19505 http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19505#Comment_19505 Sun, 08 Jul 2012 04:05:57 -0700 Joel Reyes Noche darijgrinberg comments on "Some cleaned up comments" (19504) http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19504#Comment_19504 http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19504#Comment_19504 Sun, 08 Jul 2012 02:49:25 -0700 darijgrinberg For Igor's comment to make sense, it should be noticed that the original title of the question was "If the homomorphisms are their isomorphic then they are isomorphic".

]]> Anton Geraschenko comments on "Some cleaned up comments" (19495) http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19495#Comment_19495 http://mathoverflow.tqft.net/discussion/1403/some-cleaned-up-comments/?Focus=19495#Comment_19495 Fri, 06 Jul 2012 10:10:53 -0700 Anton Geraschenko I've cleaned up the comment thread of Are there two non-isomorphic modules such that all the Hom-sets are isomorphic?. Here's a snapshot:

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This follows from Yoneda lemma if you assume this isomorphisms are natural. – Piotr Pstrągowski 21 hours ago

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Among the worst titles in my memory. – Igor Rivin 20 hours ago

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And if you do not assume the isomorphisms between Hom-sets to be natural, then for example over a field the question boils down to whether it is possible for two non-isomorphic vector spaces to have isomorphic duals. Over the field with two elements this is simply a question about the cardinality of power sets, which might very well be independant of ZFC. – Piotr Pstrągowski 20 hours ago

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@Igor: I guess it would be nice to edit the title and then inform the OP, so that next time he poses a question he would be more precise. – Chandrasekhar 12 hours ago

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Flagged Igor's comment as offensive and hate speech. – Guntram 11 hours ago

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@Guntram: You keep using that word. I do not think it means what you think it means. – Harry Gindi 9 hours ago

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I suggest "Are modules isomorphic if their Hom-sets are all isomorphic?" (or something like that). – Mark Grant 5 hours ago

@Piotr: could you please explain the "boils down" a bit further? The implication "isomorphic duals" ⟹ "all hom spaces isomorphic" seems to require some implication of the sort 2κ=2λ⟹ακ=αλ for all cardinals α. Is this true? – a-fortiori 5 hours ago

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