Geodesic
Every Grothendieck topos has a one-way site
Theory and applications of categories, Tome 16 (2006), pp. 123-126.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Lawvere has urged a project of characterizing petit toposes which have the character of generalized spaces and gros toposes which have the character of categories of spaces. Etendues and locally decidable toposes are seemingly petit and have a natural common generalization in sites with all idempotents identities. This note shows every Grothendieck topos has such a site. More, it defines slanted products which take any site to an equivalent one way site, a site where all endomorphisms are identities. On the other hand subcanonical one-way sites are very special. A site criterion for petit toposes will probably require subcanonical sites.
Classification : 18B25
Keywords: Grothendieck topos, petit topos, locale, one way site 
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Colin McLarty. Every Grothendieck topos has a one-way site. Theory and applications of categories, Tome 16 (2006), pp. 123-126. http://geodesic.mathdoc.fr/item/TAC_2006_16_a4/