Opposite category

In category theory, a branch of mathematics, the opposite category or dual category ${\displaystyle C^{\text{op}}}$ of a given category ${\displaystyle C}$ is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself. In symbols, ${\displaystyle (C^{\text{op}})^{\text{op}}=C}$. The construction can be generalized to ∞-categories using the opposite simplicial set.