"injective" terminology

[Michael Barr <barr@math.mcgill.ca>]

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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