A family of acyclic functors

Abstract

a b s t r a c tWe describe the projectives in the category of functors from a DCC poset to abelian groups. Based on this description we define a related condition, pseudo-projectivity, and we prove that this condition is enough for the vanishing of the derived direct limits. We apply this result to deduce a generalized version of Whitehead's theorem for the pushout. The dual results for inverse limits are also considered.