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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010
    • (edited Oct 15th 2012)

    am starting to work again on locally presentable (infinity,1)-category

    not much new yet, apart from some polishing. But at least the title I have finally changed, following Mike’s suggestion.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeApr 14th 2010

    That terminological issue should really bother me less than it does.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 28th 2010
    • (edited Apr 28th 2010)

    It’s locally-presentable-(,1)(\infty,1)-category-theory-day! :-)

    So I am in the process of adding material. Some things I did so far

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2010

    added the detailed proofs for why a locally presentable (oo,1)-category (defined as an accessible oo-cat with all colimits) also has all limits.

    The proof is really general abstract and relies on the (oo,1)-Yoneda lemma. So it is actually verbatim the proof that would also work for 1-categories, or for any notion of higher category that satisfies abstract category theory.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2012

    I have been trying to tidy-up locally presentable (infinity,1)-category a bit. Now I will try to fill in more details…

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 3rd 2012
    • (edited Dec 3rd 2012)

    Added the statement about transport of reflective sub-(oo,1)-categories along left adjoint \infty-functors.