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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2010
   • (edited Oct 15th 2012)
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   Author: Urs
   Format: MarkdownItexam 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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeApr 14th 2010
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   Author: Mike Shulman
   Format: MarkdownItexThat terminological issue should really bother me less than it does.

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 28th 2010
   • (edited Apr 28th 2010)
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   Author: Urs
   Format: MarkdownItexIt's locally-presentable-$(\infty,1)$-category-theory-day! :-) So I am in the process of adding material. Some things I did so far * expanded definitions and properties at [[locally presentable (infinity,1)-category]] a bit more (and more to come); * expanded [[Pr(infinity,1)Cat]] a bit more, in particular added a brief section on how to think of it as something like $\infty Vect$. * created stub for [[adjoint (infinity,1)-functor theorem]].

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

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

   • expanded definitions and properties at locally presentable (infinity,1)-category a bit more (and more to come);

   • expanded Pr(infinity,1)Cat a bit more, in particular added a brief section on how to think of it as something like $\infty Vect$.

   • created stub for adjoint (infinity,1)-functor theorem.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 3rd 2010
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   Author: Urs
   Format: MarkdownItexadded the detailed proofs for why a locally presentable (oo,1)-category (defined as an accessible oo-cat with all colimits) also <a href="http://ncatlab.org/nlab/show/locally+presentable+(infinity%2C1)-category#LimitsAndColimits">has all limits</a>. 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 15th 2012
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   Author: Urs
   Format: MarkdownItexI have been trying to tidy-up _[[locally presentable (infinity,1)-category]]_ a bit. Now I will try to fill in more details...

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

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 3rd 2012
   • (edited Dec 3rd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded the statement about _[transport of reflective sub-(oo,1)-categories](http://ncatlab.org/nlab/show/reflective+sub-%28infinity%2C1%29-category#TransportOfReflectiveSubcategories)_ along left adjoint $\infty$-functors.

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