An adjoint functor theorem

An adjoint functor theorem

[Michael Barr]

We have discovered an adjoint functor theorem that generalizes SAFT and
very nearly generalizes GAFT and I wonder if it has been noted before.

   \thm Suppose \Bsc is a wide complete category and $U:\Bsc\to\Csc$ is a
wide-limit-preserving functor.  Suppose $\Asc\inc\Bsc$ is a subcategory
that cogenerates \Bsc.  Suppose for each object $C\in\Csc$, the comma
category $(C,U|\Asc)$ has a weak initial set.  Then $U$ has a left
adjoint $F$.\eth

Michael


-- 
The modern conservative is engaged in one of man's oldest exercises in
moral philosophy--the search for a superior moral justification
for selfishness.  --J.K. Galbraith


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