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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.
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.
Yes.
Those slides by Mazel-Gee are impressive!
Okay, I have added now the missing “symmetric” in a few places.
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
See also
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