Let $\mathbf{A}$ be a category and $\mathbf{A}^{\text{op}}$ be the dual category of $\mathbf{A}$. Let $A,B$ be any two $\mathbf{A}$-object. In
this book it is written that $\operatorname{Hom}_{\mathbf{A}^{\text{op}}}(A,B)=\operatorname{Hom}_{\mathbf{A}}(B,A)$.