For each category $\mathcal{C}$ we can form a *dual category* $\mathcal{C}^{op}$. The dual category has the same objects as the original, and the same number of arrows, but all are reversed. That is given $f : A \rightarrow B$ in $\mathcal{C}$ we have $f' : B \rightarrow A$ in $\mathcal{C}^{op}$. Composition and identity is formed in the obvious way.