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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 27th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexam starting an entry _[[smooth spectrum]]_ (in the sense of _[[smooth infinity-groupoid]]_). But nothing much there yet.

   am starting an entry smooth spectrum (in the sense of smooth infinity-groupoid). But nothing much there yet.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 28th 2014
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   Author: David_Corfield
   Format: MarkdownItexAnd are there parameterized smooth spectra forming the tangent category to $Smooth \infty Grpd$, as parameterized spectra do to $\infty Grpd$?

   And are there parameterized smooth spectra forming the tangent category to $Smooth \infty Grpd$, as parameterized spectra do to $\infty Grpd$?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 28th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, that's the story already discussed at _[[tangent cohesion]]_: the tangent topos of smooth $\infty$-groupoids is the "extension" of that by the smooth spectra. I just thought that eventually this should not be hidden in the general discussion at "tangent cohesion" but get its own entry here. I hope to be expanding that entry soon. Just need to get a bunch of other items out of the way right now...

   Yes, that’s the story already discussed at tangent cohesion: the tangent topos of smooth $\infty$-groupoids is the “extension” of that by the smooth spectra. I just thought that eventually this should not be hidden in the general discussion at “tangent cohesion” but get its own entry here. I hope to be expanding that entry soon. Just need to get a bunch of other items out of the way right now…

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2014
   • (edited Apr 26th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a Properties-section _[From chain complexes of smooth modules](http://ncatlab.org/nlab/show/smooth+spectrum#FromChainComplexesOfSmoothModules)_, so far containing the proposition asserting that presheaves of $\mathbf{R} \coloneqq C^\infty(-,\mathbb{R})$-modules are already $(\infty,1)$-sheaves of spectra (without further $\infty$-stackification).

   added a Properties-section From chain complexes of smooth modules, so far containing the proposition asserting that presheaves of $\mathbf{R} \coloneqq C^\infty(-,\mathbb{R})$-modules are already $(\infty,1)$-sheaves of spectra (without further $\infty$-stackification).