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I moved the discussion which I had added under “General context” on spectrum to the page spectrum object under “In an ordinary category”.
After adding something about model structures, I guess one can add a comment like: if an (infinity,1)-category $C$ is presented by a model category $M$, then the stable (infinity,1)-category $Spt(C)$ of spectrum objects in it is presented by projective/injective model structures on the category $Spt(M)$ of spectrum objects in $M$.
Also, I guess I should move the stuff about the (Sus, Ev) adjunction to the pages suspension functor and loop functor.
Added some things to suspension (the “Suspension functor” section). The dual should be added to loop space.
Also created the stub pointed (infinity,1)-category because it was not there yet for some reason.
edit: actually I added them to suspension object, sorry.
Stub cospectrum just to record two references and links to their MR entries.
I have added to cospectrum an Idea-section, and a freely available reference with some basic theory (Hikida 81) and I cross-linked the entry with sequential spectrum and with spectrum object, so that it may be found.
I was going to ask to see if anyone could give some motivation for cospectrum to compare with that for spectrum, but looking about the latter things don’t seem so clear. I can’t see at sequential spectrum that it explains their purpose. And shouldn’t that page or spectrum at least mention ’cohomology’ and the Brown representability theorem?
So then back to cospectra, do they represent/corepresent anything?
I introduced links to Brown representability theorem at sequential spectrum and spectrum.
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