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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • (edited Nov 23rd 2009)
   • PermaLink
   Author: Urs
   Format: MarkdownI added a section <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-categorical+hom-space#enriched_homs_between_cofibrantfibrant_objects_6">Hom-spaces between cofibrant/fibrant objects</a> with a few lemmas and their proofs at [[(infinity,1)-categorical hom-space]]. (The proofs are intentionally very small-step and hopefully "pedagogical".) I also reworded the introduction part a bit and replied further in the old query box there. Effectively my point is: I am not overly happy with the title of that entry myself, but the alternatives proposed so far still strike me as worse. The main deficiency of the title is that it may sound a bit awkward. But it has the advantage of being fairly accuratively descriptive. But I won't be dogmatic about this. If there is a wide-spread desire to rename the entry, please feel free to do so.

   I added a section Hom-spaces between cofibrant/fibrant objects with a few lemmas and their proofs at

   (infinity,1)-categorical hom-space.

   (The proofs are intentionally very small-step and hopefully "pedagogical".)

   I also reworded the introduction part a bit and replied further in the old query box there.

   Effectively my point is: I am not overly happy with the title of that entry myself, but the alternatives proposed so far still strike me as worse. The main deficiency of the title is that it may sound a bit awkward. But it has the advantage of being fairly accuratively descriptive.

   But I won't be dogmatic about this. If there is a wide-spread desire to rename the entry, please feel free to do so.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI also expanded the floating toc [[model category theory - contents]] by including: - a link to [[model structure on an over category]] in the examples section - a link to [[proper model category]] in the _refinements_ section - a section _presentation of (oo,1)-categories_ with four sub-links

   I also expanded the floating toc model category theory - contents by including:

   • a link to model structure on an over category in the examples section

   • a link to proper model category in the refinements section

   • a section presentation of (oo,1)-categories with four sub-links

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • (edited Nov 23rd 2009)
   • PermaLink
   Author: Urs
   Format: Markdownreply to Toby in the query box at [[(infinity,1)-categorical hom-space]]. Maybe in the end the best is to choose whatever terminology but be sure that the punchline of the discussion we are having in that box is made an explicit _remark on terminology_ in the entry.

   reply to Toby in the query box at (infinity,1)-categorical hom-space.

   Maybe in the end the best is to choose whatever terminology but be sure that the punchline of the discussion we are having in that box is made an explicit remark on terminology in the entry.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeNov 23rd 2009
   • PermaLink
   Author: TobyBartels
   Format: MarkdownIndeed.

   Indeed.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to [[(infinity,1)-categorical hom-space]] a new sectin _[Hom-spaces of equivalences](http://ncatlab.org/nlab/show/%28infinity%2C1%29-categorical+hom-space#SpacesOfEquivalences)_ with a brief note on how the derived hom-space of equivalences in a model category is presented by the nerve of the subcategory of weak equivalences.

   I have added to (infinity,1)-categorical hom-space a new sectin Hom-spaces of equivalences with a brief note on how the derived hom-space of equivalences in a model category is presented by the nerve of the subcategory of weak equivalences.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to [[(infinity,1)-categorical hom-space]] a new section with a brief remark on its presentation by framings / simplicial Reedy resolutions (which for the moment just points to the coresponding section at [[simplicial model category]]). I have also slightly re-organized the sections such as to make it a tad more systematic. Eventually this entry deserves to be brushed up and prettified a bit more.

   I have added to (infinity,1)-categorical hom-space a new section with a brief remark on its presentation by framings / simplicial Reedy resolutions (which for the moment just points to the coresponding section at simplicial model category).

   I have also slightly re-organized the sections such as to make it a tad more systematic.

   Eventually this entry deserves to be brushed up and prettified a bit more.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded some more details on "simplicial framings" in the section _[In terms of framings / simplicial Reedy resolutions](http://ncatlab.org/nlab/show/%28infinity%2C1%29-categorical+hom-space#Framings)_. There is some duplication now with the previous section. Need to find the time to edit the entry more.

   Added some more details on “simplicial framings” in the section In terms of framings / simplicial Reedy resolutions.

   There is some duplication now with the previous section. Need to find the time to edit the entry more.

8. • CommentRowNumber8.
   • CommentAuthorZhen Lin
   • CommentTimeSep 18th 2013
   • (edited Sep 18th 2013)
   • PermaLink
   Author: Zhen Lin
   Format: MarkdownItexI added a derived functor characterisation of derived hom-spaces. Rather oddly, if $A$ is any object in a model category $M$, then the right derived functor of $M(A, -) : M \to Set$ exists... namely, $\operatorname{Ho} M(A, -) : \operatorname{Ho} M \to Set$ (even if you embed $Set$ in $sSet$ — I think this left Kan extension is preserved by any coproduct-preserving functor). I find it quite strange that by embedding $M$ in a homotopically equivalent homotopical category we can get a better answer!

   I added a derived functor characterisation of derived hom-spaces.

   Rather oddly, if $A$ is any object in a model category $M$, then the right derived functor of $M(A, -) : M \to Set$ exists… namely, $\operatorname{Ho} M(A, -) : \operatorname{Ho} M \to Set$ (even if you embed $Set$ in $sSet$ — I think this left Kan extension is preserved by any coproduct-preserving functor). I find it quite strange that by embedding $M$ in a homotopically equivalent homotopical category we can get a better answer!