Quasi-Koszulity and Minimal Horseshoe Lemma

In this paper, we mainly concentrate on the criteria for minimal Horseshoe Lemma to be true in the category of quasi-δ-Koszul modules, denoted by Qδ(R). More precisely, for a given short exact sequence ξ:0→K→M→N→0 in Qδ(R), we show that JK=K∩JM if and only if minimal Horseshoe Lemma holds with respect to ξ. Moreover, some applications of minimal Horseshoe Lemma are also given.