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In contrast with the Hovey correspondence of abelian model structures fromtwo complete cotorsion pairs, Beligiannis and Reiten give a construction ofmodel structures on abelian categories from only one complete cotorsion pair.The aim of this paper is to extend this result to weakly idempotent completeexact categories, by adding the condition of heredity of the complete cotorsionpair. In fact, even for abelian categories, this condition of heredity shouldbe added. This construction really gives model structures which are notnecessarily exact in the sense of Gillespie. The correspondence of Beligiannisand Reiten of weakly projective model structures also holds for weaklyidempotent complete exact categories.

Model structure from one hereditary complete cortorsion pair