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The monomorphism category $\mathscr{S}(A, M, B)$ induced by a bimodule$_AM_B$ is the subcategory of $\Lambda$-mod consisting of$\left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_{\phi}$ such that$\phi: M\otimes_B Y\rightarrow X$ is a monic $A$-map, where$\Lambda=\left[\begin{smallmatrix} A&M\\0&B \end{smallmatrix}\right]$. Ingeneral, it is not the monomorphism categories induced by quivers. It coulddescribe the Gorenstein-projective $\m$-modules. This monomorphism category isa resolving subcategory of $\modcat{\Lambda}$ if and only if $M_B$ isprojective. In this case, it has enough injective objects and Auslander-Reitensequences, and can be also described as the left perpendicular category of aunique basic cotilting $\Lambda$-module. If $M$ satisfies the condition ${\rm(IP)}$, then the stable category of $\mathscr{S}(A, M, B)$ admits a recollementof additive categories, which is in fact a recollement of singularitycategories if $\mathscr{S}(A, M, B)$ is a {\rm Frobenius} category.Ringel-Schmidmeier-Simson equivalence between $\mathscr{S}(A, M, B)$ and itsdual is introduced. If $M$ is an exchangeable bimodule, then an {\rm RSS}equivalence is given by a $\Lambda$-$\Lambda$ bimodule which is a two-sidedcotilting $\Lambda$-module with a special property; and the Nakayama functor$\mathcal N_\m$ gives an {\rm RSS} equivalence if and only if both $A$ and $B$are Frobenius algebras.

Bimodule monomorphism categories and RSS equivalences via cotilting modules