Brown representability follows from Rosický's theorem

We prove that the dual of a well-generated triangulated category satisfies Brown representability, as long as there is a combinatorial model. This settles the major open problem in [12]. We also prove that Brown representability holds for non-dualized well-generated categories, but that only amounts to the fourth known proof of the fact. The proof depends crucially on a new result of J. Rosický, Theory and Applications of Categories 14 (2005) no. 19, 451–479.