From page 29 of The algebra of programming :
For any category C the opposite category $C^{op}$ is defined to have the same objects and arrows as C, but the source and target operators are interchanged and composition is defined by swapping arguments:
$$ f \cdot g \text{ in } C^{op} = g \cdot f \text{ in } C. $$
This doesn't makes sense. Suppose C is the categories of all functions, and we have $f: A \leftarrow B$ and $g: B \leftarrow C$, then $g \cdot f$ doesn't even exist. Or, suppose $f: A \leftarrow B$ and $g: B \leftarrow A$, then $f \cdot g : A \leftarrow A$, and $g \cdot f : B \leftarrow B$, this is not interchanging source and target, this is changing both!