Abstract
Let R be any associative ring, n a positive integer and X a full subcategory of the category of R-modules. The monomorphism category Sn(X) of X consists of all the objects (Xi,φi), where Xi∈X for each 1⩽i⩽n, φi:Xi→Xi+1 is a monomorphism and Cokerφi∈X for each 1⩽i⩽n−1, which was introduced by Zhang. We mainly prove that there exists a recollement of the stable category Sn+1(X)_ relative to the ones Sn(X)_ and X_ for any Frobenius subcategory X and any positive integer n. To realize this purpose, we construct a recollement in the context of comma categories. As its application, it is shown that there are recollements induced by the monomorphism category of Gorenstein projective modules (resp., Ding projective modules, Gorenstein AC-projective modules, Gorenstein flat-cotorsion modules, and Gorenstein flat modules) and a hereditary Hovey triple in the category of R-modules, respectively.
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