Glat Complexes

A complex C is called glat if any morphism f from any finitely presented com-plex A to C factors through a finitely presented Gorenstein projective complex B.We first prove that the class of glat complexes is closed under direct sums,direct sum-mands,pure quotients,pure subcomplexes and direct limits,and a complex C is glat if and only if C is a direct limit of finitely presented Gorenstein projective complexes.Secondly,we explore the relationships between glat complexes and an-other complexes.At last,we investigate the existence of glat envelopes and covers of complexes.