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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2012

    created stubs for regular 2-category and exact 2-category, just so as to have this be interlinked usefully with the related entries on the nnLab.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMar 9th 2012

    Thanks! It would be fine with me (in fact, I’ve been meaning to do it for a while) to copy-and-paste material from my web on pages like this into the main lab. At the time when I first wrote it all, I was less comfortable adding things to the nLab that were at all original, and I was still working out the right definitions too, but now I’m pretty confident that these are correct.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2012
    • (edited Mar 9th 2012)

    Okay, thanks. So I have moved over now from your web the following entries

    I have edited them very slightly, adding sections where necessary, some hyperlinks, redirects, references back to your web, etc.

    I think I got most of it satisfactorily, but here and there a little more editing would be suitable. Notably there are still some long paragraphs that could do with lots more of their keywords being hyperlinked. But for the moment I am running out of steam.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeMar 13th 2012

    Thanks, this is awesome! I will probably go through and do some tweaking too when I have time.

    I have one thought: do we want to change the name of eso morphism to something like “strong 1-epic”?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2012

    change the name of eso morphism to something like “strong 1-epic”?

    Sounds good to me.

    Only that I would prefer “epi” over “epic”. (To be frank, I changed epic to epi whenever I saw an occurence. Hope you don’t mind. I feel a bit nervous about this, now that I say it, but I felt strongly that it is better this way.)

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeMar 13th 2012

    It seems that everyone agrees that ‘monic’ is an adjective while ‘mono’ (an abbreviation of ‘monomorphism’) is a noun. But many people keep using the adjective ‘epic’ as a noun instead of ‘epi’ (the abbreviation of ‘epimorphism’). So I agree with Urs … or don’t abbreviate and say strong 1-epimorphism.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 13th 2012

    many people keep using the adjective ‘epic’ as a noun

    I find myself doing that fairly often, even though I regard it as a mistake and try to catch and correct myself when it happens. Perhaps we are aided by the fact that there is this noun ’epic’, and only mathematicians recognize ’epi’ as even being a word at all. :-)

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeMar 13th 2012

    I don’t agree that “monic” is only an adjective. I don’t see any grammatical reason for “epic” and “monic” to be only adjectives and not nouns; given that they are words that mathematicians invented in the first place, don’t we get to decide what parts of speech they are? I find “epi” and “mono” rather more awkward to say that “epic” and “monic”.

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeMar 13th 2012
    • (edited Mar 13th 2012)

    Certainly one can invent words to mean whatever one wishes, but words have origins. The original words are ‘monomorphism’ and ‘epimorphism’, made by adding prefixes to ‘morphism’; the natural adjectives for these are ‘monomorphic’ and ‘epimorphic’, based on the suffix ‘-ικ-’ for Greek adjectives. Then if you want shorter adjectives, you add this suffix directly to the prefixes (dropping the vowels at the end of these prefixes in good Greek fashion), giving ‘monic’ and ‘epic’. To create shorter nouns, however, why add this suffix that makes adjectives? As long as we’re dropping the root, just use the prefixes directly: ‘mono’ and ‘epi’.

    But as you say, one can do what one wants, especially with informal abbreviations. I would put the page title at the unabbreviated strong 1-epimorphism, but all abbreviations should be (and already are) redirects. And there is ample precedent in English for using an adjective as a noun to describe a thing with the property given by that adjective, which indeed is how we got the ordinary noun ‘epic’ in the first place. It mostly just seems odd to me to stick an unnecessary (and potentially grammatically confusing) extra letter on the end of an abbreviation.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeMar 13th 2012

    Why is using a prefix as a noun more logical than using an adjective as a noun? I think part of the reason I like “monic” and “epic” is that they sound like complete words, whereas “mono” and “epi” sound like uncompleted prefixes.

    But yes, let’s use unabbreviated names for pages and redirects for all other forms.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2012
    • (edited Mar 13th 2012)

    I don’t want to be dogmatic about this and can live with either version.

    But just for the record: what bothers me about “epic” is not that it violates some pattern or rule – but that it already means something. Something very different. An “epic arrow / morphism” is… a very long arrow! Or more precisely, following my dictionary, it’s a long and adventurous arrow. :-) That sounds wrong to me, whenever I read it.

    • CommentRowNumber12.
    • CommentAuthorZhen Lin
    • CommentTimeMar 13th 2012

    Actually, epic sink sounds even more hilarious…

    • CommentRowNumber13.
    • CommentAuthorMike Shulman
    • CommentTimeMar 13th 2012

    Huh. I never had that problem. I guess to me the dictionary meaning of “epic” is so obviously irrelevant that it never occurred to me.

    • CommentRowNumber14.
    • CommentAuthorTobyBartels
    • CommentTimeMar 14th 2012

    I agree with ‘epic arrow’ and ‘epic sink’, since here ‘epic’ is an adjective. As Mike said, the ‘long and adventurous’ meaning had not occurred to me, although now I kind of like it. An epic has a broad range, after all.

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