There are some 'standard' applications of the adjoint functor
theorem (AFT) and the special adjoint functor theorem (SAFT), for
example, the existence of a free $\tau$-algebra (where
$\tau=$(operations,identities)) on a small set by the AFT,  

Stone-Cech compactification by the SAFT, and, if I am not mistaken, the proof that the category of $\tau$-algebras is cocomplete (by
using the AFT to establish a left adjoint to the appropriate diagonal
functor). 


However, I was not able to find any applications of the *duals* of
the AFT and the SAFT, neither in MacLane, nor in the Joy of
Cats. 


The Joy of Cats contains the following intriguing
remark on p. 311: 



> 
> 
> > 
> > Since many familiar categories have separators but
> >  fail to have coseparators, the dual of the Special Adjoint Functor
> >  Theorem is applicable even more often than the theorem itself.
> > 
> > 
> > 
> 
> 
> 


But what *are* the mentioned application of the dual of the SAFT?


So my questions is: **What are the 'standard' applications of the duals
of the AFT and the SAFT?** 


Googling for combinations of phrases like ''adjoint functor theorem''
and ''dual'' is not very useful, so I have tried ''dual of the adjoint
functor theorem'' and ''dual of the special adjoint functor theorem.''
This resulted in a total of 7 papers/books, from which I was not able
to get a clear answer to the current question. I have also tried in
[The Wikipedia article on adjoint
functors](http://en.wikipedia.org/wiki/Adjoint_functors), in [nLab's
article on the adjoint functor
theorems](http://ncatlab.org/nlab/show/adjoint+functor+theorem), and
in [some](https://mathoverflow.net/questions/5786/how-do-i-check-if-a-functor-has-a-left-right-adjoint)
[MO](https://mathoverflow.net/questions/6376/why-forgetful-functors-usually-have-left-adjoint/6406#6406) 
questions, but without success. 



 What are the 'standard' applications of the duals of the adjoint functor theorems?
One example is the construction of [geometric morphisms](http://ncatlab.org/nlab/show/geometric+morphism). Any colimit-preserving functor between Grothendieck toposes has a right adjoint, so if it also preserves finite limits, then it is part of a geometric morphism. Of course, in many cases in practice, the right adjoint is also easy to write down explicitly.


