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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 31st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownIn reaction to the public demand exhibited by Guillaume Brunerie's [comments](http://golem.ph.utexas.edu/category/2011/10/prequantum_physics_in_a_cohesi.html#c039962) I have created an entry [[base (infinity,1)-topos]].

   In reaction to the public demand exhibited by Guillaume Brunerie's comments I have created an entry

   base (infinity,1)-topos.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 3rd 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI would expect that infinity-topoi over base or not form a $(\infty,2)$-category. Are you saying that up-to-set theoretic problems the $(\infty,1)$-decategorification of it is in fact a $(\infty,1)$-topos ?

   I would expect that infinity-topoi over base or not form a $(\infty,2)$-category. Are you saying that up-to-set theoretic problems the $(\infty,1)$-decategorification of it is in fact a $(\infty,1)$-topos ?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> I would expect that infinity-topoi over base or not form a (∞,2)-category. Sure, if you regard $(\infty,1)Topos$ as an $(\infty,2)$-category, then all its slices are, too. > Are you saying that up-to-set theoretic problems the (∞,1)-decategorification of it is in fact a (∞,1)-topos ? No, why do you say that?

   I would expect that infinity-topoi over base or not form a (∞,2)-category.

   Sure, if you regard $(\infty,1)Topos$ as an $(\infty,2)$-category, then all its slices are, too.

   Are you saying that up-to-set theoretic problems the (∞,1)-decategorification of it is in fact a (∞,1)-topos ?

   No, why do you say that?

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeNov 3rd 2011
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   Author: zskoda
   Format: MarkdownItexOh I see: [[over-(infinity%2C1)-topos]] says it clearly.

   Oh I see: over-(infinity%2C1)-topos says it clearly.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Oh I see: over-(infinity%2C1)-topos says it clearly. I am not sure what you mean. Working over a base topos means slicing the 2-category of all toposes over a fixed base topos, not slicing a fixed topos over one of its objects. On the other hand every such over-topos has the original topos as a base topos. Is that what you are thinking of?

   Oh I see: over-(infinity%2C1)-topos says it clearly.

   I am not sure what you mean. Working over a base topos means slicing the 2-category of all toposes over a fixed base topos, not slicing a fixed topos over one of its objects.

   On the other hand every such over-topos has the original topos as a base topos. Is that what you are thinking of?