Re: an early exercise in Mac Lane

[Michael Barr <barr@barrs.org>]

I am afraid that does not work.  You have to take an identity to an
identity.  The suggested conjugation by choosing an automorphism for each
object does that.  It may be the answer Mac Lane had in mind, although
that works for any category, as noted.  I cannot think of any other
example.


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On Fri, 9 Jul 1999, john baez wrote:

> Lyle Ramshaw writes:
> 
> >   5. Find two different functors T: Grp --> Grp with object function
> >   T(G) = G the identity for every group G.
> > 
> > One such functor, of course, is the identity on every arrow as well.
> > So the challenge is to find a functor that leaves all objects
> > unchanged, but changes around at least some arrows.
> 
> > I've spent some time trying to construct a more interesting solution
> > to the exercise: a functor from Grp to Grp that leaves objects alone
> > and transforms arrows in some way that clearly changes the structure.
> > In particular, I started out hoping to take some non-null arrows to
> > null arrows.  
> 
> I assume that by "null arrow" you mean what some folks call "the trivial
> homomorphism".  
> 
> Why not go all the way and consider the functor that leaves objects
> alone and maps all arrows to null arrows?
> 
> Best,
> John Baez
> 
> 
>