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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 24th 2014
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   Author: Urs
   Format: MarkdownItexCreated [[prime spectrum of a monoidal stable (∞,1)-category]] and cross-linked vigorously with related entries. this needs to be further expand, clearly. More references etc.

   Created prime spectrum of a monoidal stable (∞,1)-category and cross-linked vigorously with related entries.

   this needs to be further expand, clearly. More references etc.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMar 24th 2014
   • (edited Mar 24th 2014)
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   Author: zskoda
   Format: MarkdownItexProbably you mean __symmetric__ (in some sense) monoidal categories as analogies of commutative rings. Already in the ring situation, the notion of a prime splits into _many_ notions which coincide (as equivalent definitions) in the commutative case and it is the whole and unfinished science which generalization is appropriate for some purpose or some class of rings.

   Probably you mean symmetric (in some sense) monoidal categories as analogies of commutative rings. Already in the ring situation, the notion of a prime splits into many notions which coincide (as equivalent definitions) in the commutative case and it is the whole and unfinished science which generalization is appropriate for some purpose or some class of rings.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 24th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes.

   Yes.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeMar 25th 2014
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   Author: David_Corfield
   Format: MarkdownItexThose slides by Mazel-Gee are impressive!

   Those slides by Mazel-Gee are impressive!

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 25th 2014
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   Author: Urs
   Format: MarkdownItexOkay, I have added now the missing "symmetric" in a few places.

   Okay, I have added now the missing “symmetric” in a few places.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 6th 2014
   • (edited Apr 6th 2014)
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   Author: Urs
   Format: MarkdownItexI have now added some pertinent references to _[[prime spectrum of a symmetric monoidal stable (infinity,1)-category]]_: *** * [[Paul Balmer]], _The spectrum of prime ideals in tensor triangulated categories_. J. Reine Angew. Math., 588:149–168, 2005 ([arXiv:math/0409360](http://arxiv.org/abs/math/0409360)) * [[Paul Balmer]], _Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings_, Algebr. Geom. Topol., 10(3):1521–1563, 2010 ([pdf](http://www.math.ucla.edu/~balmer/research/Pubfile/SSS.pdf)) Discussion of the prime spectra of the [[stable homotopy category]]/[[(∞,1)-category of spectra]] ([[finite spectrum|finite]]) is in * [[Beren Sanders]], _Higher comparison maps for the spectrum of a tensor triangulated category_ ([arXiv:1302.4521](http://arxiv.org/abs/1302.4521)) See also * [[Jack Morava]], _Toward a fundamental groupoid for the stable homotopy category_ ([arXiv:math/0509001](http://arxiv.org/abs/math/0509001))

   I have now added some pertinent references to prime spectrum of a symmetric monoidal stable (infinity,1)-category:

   ---

   • Paul Balmer, The spectrum of prime ideals in tensor triangulated categories. J. Reine Angew. Math., 588:149–168, 2005 (arXiv:math/0409360)

   • Paul Balmer, Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebr. Geom. Topol., 10(3):1521–1563, 2010 (pdf)

   Discussion of the prime spectra of the stable homotopy category/(∞,1)-category of spectra (finite) is in

   • Beren Sanders, Higher comparison maps for the spectrum of a tensor triangulated category (arXiv:1302.4521)

   See also

   • Jack Morava, Toward a fundamental groupoid for the stable homotopy category (arXiv:math/0509001)