ON THE RELATION BETWEEN K-FLATNESS AND K-PROJECTIVITY
IOANNIS EMMANOUIL
Abstract. Krause [19] has proved that the homotopy category K(R-PureProj) of pure pro- 
jective modules over an associative ring R is compactly generated and equivalent to the Verdier 
quotient K(R)/T(R), where T(R) is the triangulated subcategory of the homotopy category 
K(R) consisting of the pure acyclic complexes. We provide an alternative proof of this result. 
When restricted to the homotopy category of projective modules, this equivalence reduces to 
that obtained by Neeman [26]. As an application of this description of K(R-PureProj), we 
show that the K-flat complexes defined by Spaltenstein [28] are, up to homotopy equivalence, 
the filtered colimits of K-projective complexes of pure projective modules.