Opposite simplicial set

In higher category theory in mathematics, the opposite simplicial set (or dual simplicial set) is an operation extending the opposite category (or dual category). It generalizes the concept of inverting arrows from 1-categories to ∞-categories. Similar to the opposite category defining an involution on the category of small categories, the opposite simplicial sets defines an involution on the category of simplicial sets. Both correspond to each other under the nerve construction.