Like Michael, I've occasionally been bothered by the conflict between the two uses of "injective". However, for me it's the use of the word as a dual for "projective" that feels wrong; the opposite of "pro" is not "in" but "con" (or "contra"). Also, the use of "injective" and "surjective" for maps is so well established throughout mathematics that I don't think there is any chance of changing it. I've thought of using "coprojective" for the dual of "projective"; but for anyone with a classical education that word means "shit-throwing". Peter Johnstone ---------------------- On Tue, 18 May 2010, Michael Barr wrote:

Since there has been such a lively discussion of language (which I have kept out of because I have seen too many papers start out by saying, "By ring, we mean a commutative ring with unit"), I though I would bring up one that has long bothered me. There are too many contexts in which you have a concrete category (say of compact hausdorff spaces) in which you are dealing with both injective objects and 1-1 maps that I feel we need a better word for the latter than "injective". Of course, I could just revert to 1-1 and perhaps I will. But we have "projective" and "surjective" for the dual. This suggests "superjective", except that that is so ugly.

Any thoughts?

Michael

P.S. I originally used *-autonomous to mean symmetric and then I wrote a paper called, "Non-symmetric *-autonomous categories", so I am just as guilty.

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