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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 27th 2010
Added Todd's definition of *-quantale to quantale. Is there anything about enrichment in such things that's worth adding?
• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeFeb 27th 2010

There will be more to add about enrichment, specifically as applied to buildings, but it will take a little while to develop. In the meantime, I have added more examples of quantales and $*$-quantales, and added a small section on morphisms of quantales.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeFeb 27th 2010

Would it be worth making a separate page *-quantale?

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeFeb 27th 2010
• (edited Feb 27th 2010)

It might also be nice to say something about quantaloids, i.e. closed locally posetal bicategories, and their *-version and enrichment over those. For instance, there is Walters' theorem that sheaves on a site can be presented as categories *-enriched in a certain *-quantaloid.

• CommentRowNumber5.
• CommentAuthorTodd_Trimble
• CommentTimeFeb 28th 2010

I have made some edits to quantale, and tried submitting. The first few tries resulted in an "application error", and then the next few tries produced the message, "you cannot resubmit this form again," but apparently the edits did not go through (do not appear on the current page). I don't know what to do at this point. I have saved the contents of the page within the editor elsewhere on my computer, and will await further instructions.

• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeFeb 28th 2010

Never mind: I finagled a workaround.

• CommentRowNumber7.
• CommentAuthorTim_Porter
• CommentTimeFeb 28th 2010
• (edited Feb 28th 2010)

I noticed a similar behaviour just now when editing Cech methods. I can trace the problem in my case to the use of an accented character in a section title, which then seemed to hit problems in the TOC. That does not seem to be the case however in Quantale.

• CommentRowNumber8.
• CommentAuthorTodd_Trimble
• CommentTimeMar 3rd 2012

As a follow-up to one of Mike’s remarks here at one of the Bousfield lattice threads, I added to quantale the result that restriction to the idempotent elements in a commutative affine quantale gives the right adjoint $Idem$ to the forgetful functor from frames to commutative affine quantales. (The present point being that Bousfield classes form a commutative affine quantale under smash product.)

• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeMar 3rd 2012

Thanks!

• CommentRowNumber10.
• CommentAuthorRodMcGuire
• CommentTimeSep 24th 2017

I added the reference section quantale#automata and linked to it from the examples section.

{#automata}Relations with automata and process semantics

In the future I might incorporate more from that article when I understand it better.

• CommentRowNumber11.
• CommentAuthorpcapriotti
• CommentTimeMay 22nd 2018

I added the example of ideals of a commutative ring.