A Note on Projectively Coresolved Gorenstein Flat Complexes and Dimensions

In this article, we first establish a recollement related to projectively coresolved Gorenstein flat (PGF) complexes. Secondly, we define and study PGF dimension of complexes, we denote it PGF(X) for a complex X. It is shown that the PGF(X) is equal to the infimum of the set {supA | there exists a diagram of morphisms of complexes A←G→X, such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.