Dear Marta, I understand your concern. I want to offer the new generation the possibility of using a better terminology. Nobody is forced to adopt a new terminology. I would recommend using both terms in the introduction of a paper in topos theory. The old terminology may disappear on the long run. Best, André ________________________________ From: Marta Bunge [martabunge@hotmail.com] Sent: Saturday, November 05, 2016 1:42 PM To: Joyal, André; Thomas Streicher Cc: Martin Escardo; categories@mta.ca; Steve Vickers Subject: Re: categories: Re: Grothendieck toposes Dear Andre, I agree with you in that in that one must distinguish the notions of an elementary topos and that of a Grothendieck topos. However, I see no need for a change in terminology, as the latter (Grothendieck topos) is recovered from the former by means of the notion of a bounded geometric morphism. Topos theory is a well-established subject. A change as the one you suggest ("logos") - or any other change for that matter, is not only not necessary but in my opinion it will bring useless discussions as the one we are having now. After all, the original meaning of the name of a subject is not always adequate, but this matters little if everybody knows what is meant by it. Think that "geometry" means "measurement of the Earth", or that "Analysis" is a what was left from "Infinitesimal Analysis" after the then undesirable infinitesimals were banned and replaced by epsilons and deltas. Suppose you adopt "logos" instead of "elementary topos" and use "topos" to mean "sheaves on a site in a logos". Okay, then what? Those of us who work in Topos Theory would have the choice of accepting or rejecting your suggestion. Suppose we accept it. Then I can well imagine any paper in the area of "Logos Theory" starting with the proviso that we use "logos" in the sense of Joyal, but that it is the same concept as an elementary topos in the sense of Lawvere and Tierney. What about morphisms of logoi (logoses, logi) - geometric, logical as before, or you will also need new names for those? This is getting nowhere and I have nothing else to say on the subject. With very best regards, Marta [For admin and other information see: http://www.mta.ca/~cat-dist/ ]