On Sun, Apr 28, 2013 at 5:49 AM, Jean Bénabou <jean.benabou@wanadoo.fr> wrote: I don't like very much "setoids", and I am very tempted by "essentially
discrete" as Thomas suggested.
For these ones, I would suggest "catégories timides" or "catégories réservées", as a play on "discrete", something you could translate as "shy" or "bashful" or "shrinking categories". What would you call a category X such that the functor X --> 1 is full and
faithful? Please don't tell me what they are, I know that. I'm not even asking if there is a we'll established name for them. I don't think there is one. What I ask is: Could you suggest one? Preferably a name which would be suitable when we work with categories internal to a Topos E where supports don't split.
If you are in a playful mood, one could call them "catégories unspirées". Another suggestion is "catégories modestes". This would make a good trio with "catégories discrètes". Olivier Gérard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]