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1. • CommentRowNumber1.
   • CommentAuthorThomas Holder
   • CommentTimeOct 11th 2014
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexI've written a stub on [[Cole's theory of spectrum]] which for the time being consists largely of references and links. Further curation or correction would be appreciated!

   I’ve written a stub on Cole’s theory of spectrum which for the time being consists largely of references and links. Further curation or correction would be appreciated!

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2014
   • (edited Oct 11th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I suppose this is the abstract concept of spectrum also considered in _[[Structured Spaces]]_.

   Thanks! I suppose this is the abstract concept of spectrum also considered in Structured Spaces.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 11th 2014
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI changed some wording in the definition section ever so slightly.

   I changed some wording in the definition section ever so slightly.

4. • CommentRowNumber4.
   • CommentAuthorThomas Holder
   • CommentTimeOct 11th 2014
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexThanks! I've added some further material from the account in Johnstone 1977. There Johnstone attributes the observation of the right adjointness property of spec to Hakim. Cole's construction yields some standard examples. I don't know enough about Hakim's or Lurie's work to see how Cole's stuff is precisely related to theirs. I've added a link to [[Structured Spaces]] though.

   Thanks! I’ve added some further material from the account in Johnstone 1977. There Johnstone attributes the observation of the right adjointness property of spec to Hakim. Cole’s construction yields some standard examples. I don’t know enough about Hakim’s or Lurie’s work to see how Cole’s stuff is precisely related to theirs. I’ve added a link to Structured Spaces though.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2014
   • (edited Oct 11th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. We have an old stubby entry with the sweet name _[[locally algebra-ed topos]]_ which is effectively about this concept of "$T$-modelled topos", up so some evident variants. For the time being I have made _[[T-modelled topos]]_ redirect to that. Eventually one might split off a separate entry, or rename that existing entry, and in any case expand further (maybe by copying the relevant section from _[[Cole's theory of spectra]]_). I have added some more hyperlinks to the entry, in the first paragraphs. Regarding the entry title: a more canonical title choice might be "Cole spectrum" or maybe "spectrum of a model over a geometric theory" or the like.

   Thanks.

   We have an old stubby entry with the sweet name locally algebra-ed topos which is effectively about this concept of “$T$-modelled topos”, up so some evident variants. For the time being I have made T-modelled topos redirect to that. Eventually one might split off a separate entry, or rename that existing entry, and in any case expand further (maybe by copying the relevant section from Cole’s theory of spectra).

   I have added some more hyperlinks to the entry, in the first paragraphs.

   Regarding the entry title: a more canonical title choice might be “Cole spectrum” or maybe “spectrum of a model over a geometric theory” or the like.

6. • CommentRowNumber6.
   • CommentAuthorThomas Holder
   • CommentTimeOct 11th 2014
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexI have no problems with renaming as the title is a bit heavy. I was kind of afraid that 'Cole spectrum' suggests for one thing too much a concrete spectrum for some particular algebraic theory and too established a term, but I sure can live with it. Maybe something like 'Cole spectra' could be an alternative. Given that these words appear in Cole's title they are probably good search-engineering. So whoever has a clear preference should go ahead and rename!

   I have no problems with renaming as the title is a bit heavy. I was kind of afraid that ’Cole spectrum’ suggests for one thing too much a concrete spectrum for some particular algebraic theory and too established a term, but I sure can live with it. Maybe something like ’Cole spectra’ could be an alternative. Given that these words appear in Cole’s title they are probably good search-engineering. So whoever has a clear preference should go ahead and rename!