The Stacks project

Definition 14.12.1. An $n$-truncated simplicial object of $\mathcal{C}$ is a contravariant functor from $\Delta _{\leq n}$ to $\mathcal{C}$. A morphism of $n$-truncated simplicial objects is a transformation of functors. We denote the category of $n$-truncated simplicial objects of $\mathcal{C}$ by the symbol $\text{Simp}_ n(\mathcal{C})$.

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View Definition 14.12.1 as pdf