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, in nLab's article on the adjoint functor theorems, and in some MO questions, but without success.