Re: "injective" terminology

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

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.
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]