# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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 $\mathbf{2} = (0 \to 1)$.

• 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 $Mono$ 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, $Mono$ 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).

• CommentRowNumber8.
• CommentAuthorTodd_Trimble
• CommentTimeJun 23rd 2021

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