Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I am working on an entry model structure on orthogonal spectra. So far it contains a detailed construction of the symmetric monoidal strict model structure, and then a detailed proof of the stable model structure.
(I think its complete, but towards the end the expositional aspects need more polishing, i.e. more cross-links ect. But not today.)
This follows the writeup that I had started at Model categories of diagram spectra, but (besides being more complete and more polished by now) it works around the issue that I ran into there, by defining the weak equivalences to be the stable weak homotopy equivalences ($\pi_\ast$-isos) right away. This means that the proof still verbatim gives a proof also of the stable model structure on sequential sequential spectra and on excisive functors, but not on symmetric spectra.
I think its complete, but towards the end the expositional aspects need more polishing, i.e. more cross-links ect. But not today.
I have now expanded and polished everything up to and excluding the proof of the stable model structure, hence up to and including this summary remark on the situation for the strict model structure.
I think I have found and written out a full proof that the stable model structure on orthogonal spectra is monoidal (here).
(Couldn’t use the proof offered by MMSS00, due to that caveat)
I have added bunch of further this and that. Now i am writing a Conclusion section summarizing the constructions and theorems.
I have started a section The monoidal stable homotopy category with statement and proof of the tensor triangulated category structure; and then, using that, statement and proof of some basic properties of homotopy commutative ring spectra.
I have added a bunch of further stuff to the section Homotopy commutative ring spectra
This entry is not rendering correctly. The hyperlinked terms do not render at all at the bottom of the page. I was unable to fix this myself.
Are you referring to model structure on orthogonal spectra? That renders fine on my machine right now. But it’s a long entry, maybe I am not looking at the relevant bits.
Somebody just edited it today, after I left my previous comment. The problem was corrected by Anonymous.
I see. Now I am curious what the problem was. (In the page history one sees no visible change in Anonymous’ edit, and the previous version, rev 87, looks just fine.)
1 to 10 of 10