On 11/8/16 05:03, Thomas Streicher wrote:

On Mon, Nov 07, 2016 at 04:03:18PM -0500, Eduardo Julio Dubuc wrote:

...

Hi, in this posting I will use the terminology used by most people in the list.

There are Grothendieck, Giraud and Elementary (Lawvere-Tierney) topos.

Grothendieck are Giraud and Elementary, my question is:

Are Elementary Giraud topos which are not Grothendieck ?

But Grothendieck and Giraud toposes are the same. In the Elephant one can even find a relative Giraud Theorem.

Thomas

By Giraud topos I mean all the assumptions in Giraud's theorem, exept a small set of generators. What Grothendieck call "faux topos". See SGA4 Exposse IV Theoreme 1.2 (Giraud's theorem) and Example 2.8 (faux topos). best e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]