For two bimodules ${}_{A}N_B$ and ${}_{B}M_A$ with $M{\otimes }_{A}N=0=N{\otimes }_{B}M$, the monomorphism category $\mathcal{M}(A,M,N,B)$ and its dual, the epimorphism $\mathcal{E}(A,M,N,B)$, are introduced and studied. By definition, $\mathcal{M}(A,M,N,B)$ is the subcategory of $\mathrm{\Delta }\text{-}\mathrm{mod}$ consisting of $(X,Y,f,g)$ such that $f:M{\otimes }_{A}X\to Y$ is a monic B-map and $g:N{\otimes }_{B}Y\to X$ is a monic A-map, where $\mathrm{\Delta }=\left(\begin{array}{cc}\hfill A\hfill & \hfill N\hfill \\ \hfill M\hfill & \hfill B\hfill \\ \hfill \hfill \end{array}\right)$ is a Morita ring. This monomorphism category is a resolving subcategory of $\mathrm{\Delta }\text{-}\mathrm{mod}$ if and only if $M_A$ and $N_B$ are projective modules; and if this is the case and if in addition ${\mathrm{Hom}}_B{(N,B)}_A$ and ${\mathrm{Hom}}_A{(M,A)}_B$ are projective modules, then it has enough relative injective objects, and it is a Frobenius category if and only if A and B are selfinjective. Under these conditions we prove that there is a unique cotilting left Δ-module T, up to the multiplicity of the indecomposable direct summands, such that $\mathcal{M}(A,M,N,B)={}^{\perp }T$. When M and N are exchangeable bimodules, Ringel-Schmidmeier-Simson equivalence between $\mathcal{M}(A,M,N,B)$ and $\mathcal{E}(A,M,N,B)$ are given.

对于两个双模块 ${}_{\mathrm{一种}}ñ_{乙}$ 和 ${}_{乙}\mathrm{中号}_{\mathrm{一种}}$ 与 $\mathrm{中号}{\otimes }_{\mathrm{一种}}ñ=0=ñ{\otimes }_{乙}\mathrm{中号}$，单态类别 $\mathcal{中号}（\mathrm{一种}，\mathrm{中号}，ñ，乙）$ 及其对偶 $\mathcal{Ë}（\mathrm{一种}，\mathrm{中号}，ñ，乙）$介绍和研究。根据定义，$\mathcal{中号}（\mathrm{一种}，\mathrm{中号}，ñ，乙）$ 是的子类别 $\mathrm{\Delta }\text{--}\mathrm{模}$ 包含由...组成 $（X，ÿ，F，G）$ 这样 $F：\mathrm{中号}{\otimes }_{\mathrm{一种}}X\to ÿ$是monic B -map和$G：ñ{\otimes }_{乙}ÿ\to X$是单项A映射，其中$\mathrm{\Delta }=（\begin{array}{cc}\hfill \mathrm{一种}\hfill & \hfill ñ\hfill \\ \hfill \mathrm{中号}\hfill & \hfill 乙\hfill \\ \hfill \hfill \end{array}）$是森田戒指 此单态类别是的解析子类别$\mathrm{\Delta }\text{--}\mathrm{模}$ 当且仅当 ${\mathrm{中号}}_{\mathrm{一种}}$ 和 ${ñ}_{乙}$是投射模块；如果是这种情况，以及是否另外${\mathrm{坎}}_{乙}{（ñ，乙）}_{\mathrm{一种}}$ 和 ${\mathrm{坎}}_{\mathrm{一种}}{（\mathrm{中号}，\mathrm{一种}）}_{乙}$是射影模块，则它具有足够的相对内射对象，并且仅当A和B为自射时才属于Frobenius类别。在这些条件下，我们证明存在一个唯一的剩余Δ-模T，直至不可分解的直接被加数的多重性，使得$\mathcal{中号}（\mathrm{一种}，\mathrm{中号}，ñ，乙）={}^{\perp }Ť$。当M和N是可交换双模时，Ringel-Schmidmeier-Simson等价$\mathcal{中号}（\mathrm{一种}，\mathrm{中号}，ñ，乙）$ 和 $\mathcal{Ë}（\mathrm{一种}，\mathrm{中号}，ñ，乙）$ 给出。