Cosimplicial resolutions and homotopy spectral sequences in model categories.
Let and be abelian categories with enough projective and injective objects, and a left exact additive functor. Then one has a comma category . It is shown that if is -exact, then is a (hereditary) cotorsion pair in and ) is a (hereditary) cotorsion pair in if and only if is a (hereditary) cotorsion pair in and and are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories and can induce special preenveloping classes...