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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-$(\infty,1)$-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.