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• CommentRowNumber1.
• CommentTimeFeb 6th 2014
• (edited Feb 6th 2014)

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.

• CommentRowNumber2.
• CommentTimeFeb 6th 2014
• (edited Feb 7th 2014)

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.

• CommentRowNumber3.
• CommentTimeFeb 7th 2014
• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeSep 4th 2017

Stub cospectrum just to record two references and links to their MR entries.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 4th 2017
• (edited Sep 4th 2017)

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.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeSep 5th 2017

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?

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeSep 6th 2017