I like Todd's suggestion of "amphimorphic". It goes well with the "ambilocales" that I invented a few years back but abandoned, though I intend to take them up again since Reinhold Heckmann recently drew to my attention to the fact that all countably presented locales are spatial, which was apparently first proved by Mike Fourman and Robin Grayson. However, you cannot dislodge the phrase "schizophrenic object". There are professional and sound intellectual reasons for citing Chapter VI, Section 4 of Peter Johnstone's book, "Stone Spaces". My point is that, once you have used the word in this citation, it will probably be unnecessary use it ever again in a paper, or indeed in an entire research programme. For example, although ASD was motivated in part by this idea, only the logically first paper and the survey actually use the word, twice each. This is in contrast, for example, to my proposal of "prone" to replace "cartesian" in the theory of fibred categories, where this notion needs to be used in almost every other sentence. Tom quotes the Guardian [newspaper]'s guide to style. Of course it is wrong to say "schizophrenic" when you mean "in two minds". But this is for the same reason as most journalists' uses of "epicentre" and "begs the question" are wrong. These words and phrases have technical or precise meanings, which are destroyed if the word is used in a casual sense without this meaning. Is there a serious danger of confusing the technical meanings of "schizophrenic" in category theory and psychiatry? Especially considering that our concept is only going to be used by someone who already has a pretty sophisticated understanding of the big picture of mathematics? The word is unlikely ever to find its way into popular or recreational mathematics. In fact, a very large proportion of my time is now being taken up by the affairs of someone with dementia and paranoia. I was on the phone to the psychiatric hospital this morning. I am about to "steal" some time to think about "ambilocales". Am I really likely to get confused between these two domains in which the word "schizophrenic" might be used? Paul [For admin and other information see: http://www.mta.ca/~cat-dist/ ]