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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2010
   • (edited Dec 21st 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexam starting to work on [[derived smooth manifold]], so far just a little bit on the motivation (correction of limits of manifolds) I am a bit hesitant to add a lot of details from David Spivak's article, since it seems evident that there is some room to streamline the constructions. I need to think about how to deal with this. One really wants to just specify the site as a [[geometry (for structured (infinity,1)-toposes)]] and then just say that a derived manifold is a derived scheme in the sense descrived at [[generalized scheme]] on this. In section 10.1 David Spivak discusses one reason that prevented him from setting things up this way: actually I think this points to the following general issue with the definition of [[geometry (for structured (infinity,1)-toposes)]]: instead of a Grothendieck topology generated by admissible morphisms the definition ought to just refer to a _coverage_ by admissible morphisms, and instead of the stability under pullback one ought to just consider the coverage-style stability condition. More later.

   am starting to work on derived smooth manifold, so far just a little bit on the motivation (correction of limits of manifolds)

   I am a bit hesitant to add a lot of details from David Spivak’s article, since it seems evident that there is some room to streamline the constructions. I need to think about how to deal with this. One really wants to just specify the site as a geometry (for structured (infinity,1)-toposes) and then just say that a derived manifold is a derived scheme in the sense descrived at generalized scheme on this.

   In section 10.1 David Spivak discusses one reason that prevented him from setting things up this way: actually I think this points to the following general issue with the definition of geometry (for structured (infinity,1)-toposes): instead of a Grothendieck topology generated by admissible morphisms the definition ought to just refer to a coverage by admissible morphisms, and instead of the stability under pullback one ought to just consider the coverage-style stability condition.

   More later.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[David Carchedi]], *Derived Manifolds as Differential Graded Manifolds* &lbrack;[arXiv:2303.11140](https://arxiv.org/abs/2303.11140)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/derived+smooth+manifold/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/derived+smooth+manifold/18">v18</a>, <a href="https://ncatlab.org/nlab/show/derived+smooth+manifold">current</a>

   added pointer to today’s

   • David Carchedi, Derived Manifolds as Differential Graded Manifolds [arXiv:2303.11140]

   diff, v18, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeMar 21st 2023
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded * [[David Carchedi]], Pelle Steffens, _On the universal property of derived manifolds_ &lbrack;[arXiv:1905.06195](https://arxiv.org/abs/1905.06195)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/derived+smooth+manifold/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/derived+smooth+manifold/19">v19</a>, <a href="https://ncatlab.org/nlab/show/derived+smooth+manifold">current</a>

   Added

   • David Carchedi, Pelle Steffens, On the universal property of derived manifolds [arXiv:1905.06195]

   diff, v19, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Pelle Steffens]], *Derived $C^\infty$-Geometry I: Foundations* &lbrack;[arXiv:2304.08671](https://arxiv.org/abs/2304.08671)&rbrack; (the list of references should be organized better...) <a href="https://ncatlab.org/nlab/revision/diff/derived+smooth+manifold/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/derived+smooth+manifold/21">v21</a>, <a href="https://ncatlab.org/nlab/show/derived+smooth+manifold">current</a>

   added pointer to:

   • Pelle Steffens, Derived $C^\infty$-Geometry I: Foundations [arXiv:2304.08671]

   (the list of references should be organized better…)

   diff, v21, current