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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 27th 2014

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

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 28th 2014

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

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    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…

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2014
    • (edited Apr 26th 2014)

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