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For a triangulated category with products we develop a method forconstructing a nice set of cogenerators, allowing us to prove a formalcriterion in order to satisfy Brown representability for covariant functors. Weapply this criterion for showing that both homotopy category of projectivemodules and homotopy category of projective objects in a category of functorsfrom a small category to a module category satisfy this kind ofrepresentability. In particular, homotopy category of projective complexessatisfies Brown representability for covariant functors.

Constructing cogenerators in triangulated categories and Brown representability