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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2018

    The entry used to be a plain disambiguation between reflective subcategory and an empty list of other meaning of reflection.

    But since the only evident point that entries like rotation, translation, boost, etc. could point to for related concepts is an entry called reflection. So maybe that should be the main meaning here, and alternative meaning be secondary.

    I slightly edited accordingly. But besides the different link structure now, there is still no substantial content here.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 17th 2018

    I’ll edit when I have a chance, but I’d rather say something about reflection across a hyperplane etc. in the Idea section. An involutive linear transformation that fixes a hyperplane, or something like that (what’s in the Idea section currently doesn’t seem correct).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2018

    Sure, okay, I wrote a more decent sentence.

    But I don’t have the energy to write an entry about reflections now, for the time being I just wanted to fix the link structure of the entries.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeApr 17th 2018

    It would, of course, be possible to name a page something like reflection in a hyperplane or reflection transformation, and keep reflection as a disambiguation (or even a redirect to reflective subcategory). I suspect that there are more links on the nLab that want to point reflection to reflective subcategory than ones which use the transformation sense (even though this is probably the opposite of mathematics in general), so I would somewhat prefer this. We have a similar reversal with conjunction and logical conjunction.

    • CommentRowNumber5.
    • CommentAuthorRichard Williamson
    • CommentTimeApr 17th 2018
    • (edited Apr 17th 2018)

    Not that it is of much relevance, but I’d just thought I’d mention that there is also a programming language concept called ’reflection’. It typically refers to ’self-examination’ of, and de facto modification of, code at runtime, e.g. one might look up at runtime the methods that a particular class has. A notable use of it is for example in ’mocking’ when unit testing.

    Edit: I realised afterwards that everything I wrote is covered in the wikipedia article on this!

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2018
    • (edited Apr 18th 2018)

    I suspect that there are more links on the nLab that want to point reflection to reflective subcategory than ones which use the transformation sense

    Searching with

      reflection site:ncatlab.org
    

    seems to show that no page actually points to the entry “reflection”, except my cross-links with the related geometric concepts. All the category theoretic entries use the word without hyperlinking it.

    For example at reduced simplicial set it has a section titled “Reflection” which then links to “reflective subcategory”.

    I feel that regarding “reflection” as not primarily associated with the geometric concept is a specialization fallacy which we should not fall into lest the intellectual scope of the nLab will appear to be rather narrow. But if you feel very unhappy with the entry not being a disambiguation in the way it was before, I”ll roll it back.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 18th 2018

    I think linear reflection could be a good title for the intended content.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeApr 18th 2018

    I’m certainly not “very unhappy”; if you feel strongly that it should be this way, then let’s keep it this way. I stand corrected about links to “reflection”; on further reflection (hah) that makes sense, as probably usually when the concept is first introduced in any discussion it is likely to be by way of the reflective subcategory rather than the reflection functor. Also reflector does redirect to reflective subcategory, so we can always use that instead.

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