Re: Terminological question, and more

["Fred E.J. Linton" <fejlinton@usa.net>]

Thanks to all who've responded.

> I've been asked for "... the name given in an arbitrary category
> to an object A for which every mono B----->A is an isomorphism."

Peter Johnstone has suggested that such an object (whose poset of
subobjects reduces to just the object itself) is simply "minimal".

And I'm embarrassed at having lost so much of my former grasp of Galois
theory:

> ... whether "the inclusion Q >-------> R of
> the ring of rational numbers into that of real ones is a bimorphism, in  the
> category Rng of rings with units and units preserving ring homomorphisms."
>
> Reflexively I think: monic, yes; epic, no, as permuting any two independent
> transcendentals should extend to a non-identity automorphism of R over Q.

No! There is no "non-identity automorphism of R over Q."  Fortunately,
as Mike Barr and George Janelidze have pointed out, each permutation of a  
transcendence basis of R over Q extends to an injection, over Q, of R 
into its algebraic closure C, which is good enough.

Cheers, and thanks again, -- Fred



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