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I created adequate subcategory. However, once I’d done so then I found it linked from dense functor and after reading that I wasn’t sure I ought to have created the original page. I did so because I wanted to record Isbell’s idea as it’s fairly relevant to categories of generalised smooth spaces - the test spaces form an adequate subcategory (or sort of do, I need to work out the details).
It seems to be old terminology (reading dense functor) so maybe a page devoted to it isn’t right. I could shift it to dense functor?
Just as a historical note: “adequate” is indeed somewhat old-fashioned terminology, and dense subcategory or dense functor is more common these days. I won’t weigh in on whether it should be moved.
I’m a little surprised that dense functor didn’t already redirect that title. I would vote for merging the content into dense functor.
Sounds good to me. I’ll do it tomorrow.
Query box from dense functor
Mike: Would it be possible to have one page about dense subcategories in the canonical-colimit sense, and a different page about dense subcategories in the shape-theory sense, which only refer to each other briefly as a different meaning of the word? If one never talks about a dense functor in shape theory, then maybe all the shape-theoretic stuff could be on the page dense subcategory and the canonical-colimit stuff on this page. Or we could be like Wikipedia and have dense subcategory (shape theory) and, uh, the other one.
Toby: What about adequate subcategory? Or is that outdated?
Mike: Yes. I’ve never heard any modern source use that word.
I’ve shifted most of what I put at adequate subcategory to dense functor. I wasn’t sure enough I’d get all the ops right to be able to say what right adequate should map to so that’s a bit vague and I left out the examples that were right adequate. Isbell also had a notion of proper adequate which had something to do with size. I’ve left that out for now. The old page is now adequate subcategory > history and adequate subcategory should redirect to dense functor.
Except, of course, the cache bug hit and it didn’t get expired.
I think right adequate = codense (= the opposite functor is dense).
That felt like the obvious name, but as it wasn’t already on the page then I didn’t want to invent it.
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