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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 24th 2014

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.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeMar 24th 2014
• (edited Mar 24th 2014)

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 24th 2014

Yes.

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeMar 25th 2014

Those slides by Mazel-Gee are impressive!

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 25th 2014

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 6th 2014
• (edited Apr 6th 2014)

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

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