Dual Category

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.