  Baer's Criterion of injectivity implies that injectivity of a module is a
factorization property w.r.t. a single monomorphism. Using the notion of a
cotorsion pair, we study generalizations and dualizations of factorization
properties in dependence on the algebraic structure of the underlying ring $R$
and on additional set-theoretic hypotheses. For $R$ commutative noetherian of
Krull dimension $0 < d < \infty$, we show that the assertion `projectivity is a
factorization property w.r.t. a single epimorphism' is independent of ZFC +
GCH. We also show that if $R$ is any ring and there exists a strongly compact
cardinal $\kappa > |R|$, then the category of all projective modules is
accessible.
