simplicial object

Let \(\mathcal{C}\) be a category and \(\Delta\) the simplex category. A simplicial object is a contravariant functor

\begin{align*} \mathcal{F}: \Delta \rightarrow \mathcal{C} \end{align*}

where the

• face map (category theory)
• degeneracy map (category theory)

satisfy the simplicial identity see: C-valued presheaf