Dear Jean,

As many of you I presume, I have for ages, and very often, had to deal with categories which are both groupo?ds and posets, or again which are equivalent to a discrete category. Is there a well established name for them?

What about "essentially discrete" like in "essentially small" or "essentially surjective". Generally, for any property P of categories I would say a category is "essentially P" if it is equivalent to a category with property P. So "essentially" is a kind of magic word transforming "evil" properties into "non-evil" ones. (I don't think one should always do this!) Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]