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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 5th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexa stub entry, for the moment just so as to give a home to these two references: * [[Hiroshi Kihara]], _Model category of diffeological spaces_, Journal of Homotopy and Related Structures, (2018), 1-40 ([arXiv:1605.06794](https://arxiv.org/abs/1605.06794)) * [[Tadayuki Haraguchi]], [[Kazuhisa Shimakawa]], _A model structure on the category of diffeological spaces_ ([arXiv:1311.5668](https://arxiv.org/abs/1311.5668)) <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/1">v1</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   a stub entry, for the moment just so as to give a home to these two references:

   • Hiroshi Kihara, Model category of diffeological spaces, Journal of Homotopy and Related Structures, (2018), 1-40 (arXiv:1605.06794)

   • Tadayuki Haraguchi, Kazuhisa Shimakawa, A model structure on the category of diffeological spaces (arXiv:1311.5668)

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added commentary to the References-items ([here](https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces#References)), in an attempt to make transparent the somewhat inconclusive state of the literature on this topic <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+diffeological+spaces/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/4">v4</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   I have added commentary to the References-items (here), in an attempt to make transparent the somewhat inconclusive state of the literature on this topic

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have now also added a bit of text on the state of the art to the Idea-section. Then I included the discussion of the strategy via factorization through D-topological spaces. A minute ago I received a kind email from the authors of the model structure with respect to the "correct" smooth homotopy groups: They acknowledge that there was indeed a gap in their previous proof, but say that they have fixed it and are about to have a new article out. <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+diffeological+spaces/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/5">v5</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   I have now also added a bit of text on the state of the art to the Idea-section. Then I included the discussion of the strategy via factorization through D-topological spaces.

   A minute ago I received a kind email from the authors of the model structure with respect to the “correct” smooth homotopy groups: They acknowledge that there was indeed a gap in their previous proof, but say that they have fixed it and are about to have a new article out.

   diff, v5, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 26th 2020
   • (edited Nov 26th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItex...and now the announced article is available, have now added pointer to it in the entry: * [[Tadayuki Haraguchi]], [[Kazuhisa Shimakawa]], _A model structure on the category of diffeological spaces, I_ ([arXiv:2011.12842](https://arxiv.org/abs/2011.12842)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+diffeological+spaces/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/6">v6</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   …and now the announced article is available, have now added pointer to it in the entry:

   • Tadayuki Haraguchi, Kazuhisa Shimakawa, A model structure on the category of diffeological spaces, I (arXiv:2011.12842)

   diff, v6, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 15th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Hiroshi Kihara]], *Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces* ([arXiv:1702.04070](https://arxiv.org/abs/1702.04070)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+diffeological+spaces/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/7">v7</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   added pointer to:

   • Hiroshi Kihara, Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces (arXiv:1702.04070)

   diff, v7, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 18th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexTadayuki Haraguchi informs me that [arXiv:2011.12842](https://arxiv.org/abs/2011.12842) has now been refereed and accepted at the Mathematical Journal of Okayama University, which suggests that the gap it set out to address has been filled for good. <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+diffeological+spaces/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+diffeological+spaces/8">v8</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+diffeological+spaces">current</a>

   Tadayuki Haraguchi informs me that arXiv:2011.12842 has now been refereed and accepted at the Mathematical Journal of Okayama University, which suggests that the gap it set out to address has been filled for good.

   diff, v8, current