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nLab > Latest Changes: ETCC/ET2CC

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    • CommentRowNumber1.
    • CommentAuthorThomas Holder
    • CommentTimeJul 28th 2014

    I have expanded on ETCC and introduced a section on ET2CC which I could occasionally fill with Mike’s ideas from MO in case all n-categorists are lying on the beach. I would also propose to replace the current ’idea’ section with what is right now called ’overview’ or some reworking of that.

    I think it best to keep everything in a single entry given that these ideas on ETCC with or without 2 meet only a limited enthusiasm in the HOTT times.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 28th 2014

    Looking good so far!

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJul 28th 2014

    Yes, looks good, thanks! In general, I think there is no reason for “current enthusiasm” to dictate what should be a separate entry; if two things are separate concepts, they deserve separate entries as long as we have enough content for both (or are willing for one of them to be a stub). But it’ll be a while before I have time either for adding to this myself or for lying on the beach.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 28th 2014

    “lying on the beach” – learned allusion to Smale’s preferred way of working?? Or something else?

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 28th 2014

    @Todd, are you asking me or Thomas? I was just pointing out that n-category theorists might be occupied with something other than lying on the beach.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 28th 2014

    I was asking Thomas. But anyone is welcome to answer. :-)

    nn-category theorist or just plain human being, I don’t have time for lying on the beach either. :-)

    • CommentRowNumber7.
    • CommentAuthorThomas Holder
    • CommentTimeJul 28th 2014
    1. I would never reproach to anybody’s lying on the beach.
    2. Mike wasn’t among the usual suspects anyway, as I have heard a busy bee at elegant Reedy category.
    3. No allusion to Steve S. crossed my mind.
    4. I think that keeping a single entry might enhance the readership for ET2CC at the moment.
    5. the ET2CC part is done! mostly by copy&paste with additional garland decorations. It’s open for slaughter or shall we say improvement?
    6. I herewith officially resign from my temporary office as n-categorical foundamentalist and ask some n-wizard to kindly provide the correct link to ’2-categorical logic’ within the quote from Mike, I don’t know how to do this.
    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 29th 2014

    I’m being slightly lazy and not checking, but do we know that the codomain of the classifying discrete opfibration is a model of ETCS? Or perhaps the discrete opfibration is a universe object?

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeJul 29th 2014

    Re #7.6, link added.

    @DavidR, a classifying discrete opfibration certainly won’t automatically model ETCS, but one should be able to assume additional axioms that ensure it does.

    • CommentRowNumber10.
    • CommentAuthorThomas Holder
    • CommentTimeJul 29th 2014

    Thanks for fixing the link! I’ve finally given more prominence to the MO-link in the reference section as it nicely compelements the nlab-entry.

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