3 Nov
2016
3 Nov
'16
4:45 a.m.
The very notion of Grothendieck topos involves in fact two topos (sheaves over a site on the base). That is, it is a notion of geometric morphism, it does not make sense as a single category. The notion of elementary topos is a completely different notion which involves a single topos, it does perfect sense as a single category. This observation was made to me by Jacques Penon about 36 years ago. I agree with Joyal that the two notions should be kept apart. Not doing so has created a lot of confusion. best e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]