On λ-pure acyclic complexes in a Grothendieck category.

Abstract Let A be a Grothendieck category. We prove that there is an infinite regular cardinal λ such that A has λ -pure injective envelopes. Furthermore, we show that any λ -pure acyclic complex in A is a directed union of contractible subcomplexes. This provides an answer to a question which is conjectured by Simson in [14, Conjecture 3.4]. [ABSTRACT FROM AUTHOR]