Re: Regular embedding

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

I certainly welcome Ross' clarification of his problem.  One possibility
would be to give the proof except for the existence of sufficient regular
functors and either refer the students to the paper or (better) write it
out carefully and distribute it.  One thing I have given only a little
thought to is whether it can be done using a maximal principle argument.
The point is that it is not a question of extending a map to a larger and
larger subobject, but of building larger and larger objects and not as
subobjects of something already given.  This makes it different from the
proof, say, that divisible abelian groups are injective (from which the
existence of sufficient injectives in any module category follows easily).
I think a maximal principle argument goes down a lot more easily than one
based overtly on ordinals or transfinite induction.

Ross, it sounds like a beautiful course and if you have notes, I would
like to see them. 

Michael