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I’ve added Peter May’s Galois theory example to M-category in a section “Applications”.
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 $\mathbf{2} = (0 \to 1)$.
Nice! I guess maybe that is in some sense ’the simplest nontrivial Grothendieck quasitopos’?
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).
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.
I’ve updated M-category#definitions slightly to give M the alternative name $Mono$ and mention the Sierpinski topos.
should it also be mentioned that it contains the double negation topology separated presheaves?
Well, $Mono$ is the category of $\neg\neg$-separated presheaves in $Set^\to$. And yes, that’s worth mentioning on the page (which I’ve now done).
Created Related Concepts section; added relative category and F-category.
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