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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeDec 23rd 2011

    I’ve added Peter May’s Galois theory example to M-category in a section “Applications”.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 10th 2013

    I added the observation to M-category that \mathcal{M} is a Grothendieck quasitopos (which is something that had never actually occurred to me before yesterday). In fact it can be described as the category of ¬¬\neg \neg-separated presheaves on 2=(01)\mathbf{2} = (0 \to 1).

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeMar 11th 2013

    Nice! I guess maybe that is in some sense ’the simplest nontrivial Grothendieck quasitopos’?

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeMar 11th 2013

    Technical note: When you link to a particular section of an nLab page, you should give that section a permanent name (in the HTML), because the automatic section names may change.

    So #### Example: $Subset$ becomes #### Example: $Subset$ {#Subset} (for example).

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 11th 2013

    Thanks, Mike! And yes, probably. (Only at length am I getting better at instinctively knowing whether a category is a quasitopos.)

    And thanks very much, Toby – I forgot to do that.

    • CommentRowNumber6.
    • CommentAuthorRodMcGuire
    • CommentTimeSep 6th 2017
    • (edited Sep 6th 2017)

    I’ve updated M-category#definitions slightly to give M the alternative name MonoMono and mention the Sierpinski topos.

    should it also be mentioned that it contains the double negation topology separated presheaves?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 6th 2017
    • (edited Sep 6th 2017)

    Well, MonoMono is the category of ¬¬\neg\neg-separated presheaves in Set Set^\to. And yes, that’s worth mentioning on the page (which I’ve now done).

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 23rd 2021

    Created Related Concepts section; added relative category and F-category.

    diff, v21, current

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeMay 21st 2022

    Mention Kleisli categories as an example.

    diff, v22, current