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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 9th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated [[model structure on dg-categories]]

   created model structure on dg-categories

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 20th 2014
   • (edited Mar 20th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe entry _[[model structure on dg-categories]]_ long used to say "this should be a presentation of the $\infty$-category of (linear) stable $\infty$-categories ". In fact it is, if one is careful not to use the Dwyer-Kan-type weak equivaelences but Morita equivalences. This folk theorem was finally spelled out in some detail in * [[Lee Cohn]], _Differential Graded Categories are k-linear Stable Infinity Categories_ ([arXiv:1308.2587](http://arxiv.org/abs/1308.2587)) and I have added pointers to this article now to the above entry as well as to _[[stable (infinity,1)-category]]_ and to a bunch of related entries on dg-categories.

   The entry model structure on dg-categories long used to say “this should be a presentation of the $\infty$-category of (linear) stable $\infty$-categories “.

   In fact it is, if one is careful not to use the Dwyer-Kan-type weak equivaelences but Morita equivalences.

   This folk theorem was finally spelled out in some detail in

   • Lee Cohn, Differential Graded Categories are k-linear Stable Infinity Categories (arXiv:1308.2587)

   and I have added pointers to this article now to the above entry as well as to stable (infinity,1)-category and to a bunch of related entries on dg-categories.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * Piergiorgio Panero, Boris Shoikhet, _A Quillen model structure on the category of Kontsevich-Soibelman weakly unital dg categories_ ([arXiv:1907.07970](https://arxiv.org/abs/1907.07970)) * Piergiorgio Panero, Boris Shoikhet, _A closed model structure on the category of weakly unital dg categories, II_ ([https://arxiv.org/abs/2007.12716](https://arxiv.org/abs/2007.12716)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-categories/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-categories/14">v14</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-categories">current</a>

   added pointer to

   • Piergiorgio Panero, Boris Shoikhet, A Quillen model structure on the category of Kontsevich-Soibelman weakly unital dg categories (arXiv:1907.07970)

   • Piergiorgio Panero, Boris Shoikhet, A closed model structure on the category of weakly unital dg categories, II (https://arxiv.org/abs/2007.12716)

   diff, v14, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have merged some material from a duplicate page into this one here (following discussion [there](https://nforum.ncatlab.org/discussion/8553/model-structures-on-dgcategories-history/?Focus=110591#Comment_110591)), though most material was already contained here and in more detail (which is not to say that this entry here wouldn't deserve more attention) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-categories/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-categories/15">v15</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-categories">current</a>

   I have merged some material from a duplicate page into this one here (following discussion there), though most material was already contained here and in more detail (which is not to say that this entry here wouldn’t deserve more attention)

   diff, v15, current