Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthoradeelkh
   • CommentTimeFeb 6th 2014
   • (edited Feb 6th 2014)
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexI 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]].

   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.

2. • CommentRowNumber2.
   • CommentAuthoradeelkh
   • CommentTimeFeb 6th 2014
   • (edited Feb 7th 2014)
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexAdded 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthoradeelkh
   • CommentTimeFeb 7th 2014
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexAdded [[symmetric monoidal structure on spectrum objects]], [[graded monoid]], [[symmetric endofunctor]]. Updates to [[spectrum object]], [[suspension object]].

   Added symmetric monoidal structure on spectrum objects, graded monoid, symmetric endofunctor. Updates to spectrum object, suspension object.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeSep 4th 2017
   • PermaLink
   Author: zskoda
   Format: MarkdownItexStub [[cospectrum]] just to record two references and links to their MR entries.

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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 4th 2017
   • (edited Sep 4th 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to _[[cospectrum]]_ an Idea-section, and a freely available reference with some basic theory ([Hikida 81](https://ncatlab.org/nlab/show/cospectrum#Hikida81)) and I cross-linked the entry with _[[sequential spectrum]]_ and with _[[spectrum object]]_, so that it may be found.

   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.

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 5th 2017
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI 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 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?

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 6th 2017
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI introduced links to [[Brown representability theorem]] at [[sequential spectrum]] and [[spectrum]].

   I introduced links to Brown representability theorem at sequential spectrum and spectrum.