# 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

## Discussion Tag Cloud

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

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 8th 2013

I have splitt off from classifying topos an entry classifying topos for the theory of objects and added the statement about the relation to finitary monads.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeAug 8th 2013

I added to your remark a related point of view, and linked to some notes of mine.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 8th 2013
• (edited Aug 8th 2013)

Ah, thanks, that’s nice!!

We should add some kind of remark concerning $[\mathbb{P}^{op}, Set]$ also as an Example at monoidal topos. And I guess we should still add a pointer to an explanation of $\mathbb{P}$ to the entry. I can’t right now, though, am in a rush here…

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeAug 8th 2013

Nice page, thanks.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 9th 2013

I have added a stub for permutation category, just for completeness. In the course of this I noticed that we already have braid category! I have now cross-linked that a bit more such as to make it easier to find.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 26th 2014
• (edited Nov 26th 2014)

Spelled out here the argument for why $PSh(FinSet^{op})$ is the classifying topos for objects by pointing to this fact.

(Just for completeness.)

Also added the remark that similarly $PSh((FinSet_\ast)^{op})$ is the classifying topos for pointed objects.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 26th 2014

added also at classifying topos for the theory of objects remarks on the $\infty$-case:

Similarly

• $PSh(FinSet_\ast^{op})$ is the classifying topos for pointed objects.

• write $Fin\infty Grpd$ for the full sub-(∞,1)-category on ∞Grpd which is generated under finite (∞,1)-colimits from the point $\ast$ (HA, def. 1.4.2.8), then the (∞,1)-presheaf (∞,1)-topos $PSh_\infty(Fin\infty Grpd^{op})$ is the classifying (∞,1)-topos for objects;

• write $Fin\infty Grpd_\ast$ for pointed finite $\infty$-groupoids in this sense, then $PSh_\infty((Fin\infty Grpd_\ast)^{op})$ is the classifying $(\infty,1)$-topos for pointed objects. See also at spectrum object via excisive functors.

• Added remarks on “finite” in FinSet.
• Added remarks on object classifier as generalized space of “sets”

Steve Vickers

1. Added more concrete construction of the pointed set classifier.

Steve Vickers

• CommentRowNumber10.
• CommentAuthorThomas Holder
• CommentTimeNov 27th 2018

Fixed some typos and highlighted (hopefully in a correct way) the role of the category of elements in this. It would be nice if one could bring the description of the generic object in section 2 notationally and conceptually in line with the description given in the current section 3 ! Thanks anyway for polishing the entries on ’geometric’ logics and adding clarifications !

• CommentRowNumber11.
• CommentAuthorDavidRoberts
• CommentTimeNov 27th 2018

Linked to the page finite set in the comments about what finite sets are meant for $[FinSet, Set]$.