Remark 8.1.3.2. Let $n \geq 0$ be an integer. Then the simplicial set $\operatorname{Tw}( \Delta ^{n} )$ can be identified with the nerve of the partially ordered set $Q = \{ (i,j) \in [n]^{\operatorname{op}} \times [n]: i \leq j \} $ (see Example 8.1.0.5). Consequently, if $\operatorname{\mathcal{C}}$ is an arbitrary simplicial set, then $n$-simplices of $\operatorname{Cospan}(\operatorname{\mathcal{C}})$ can be identified with morphisms $\operatorname{N}_{\bullet }(Q) \rightarrow \operatorname{\mathcal{C}}$, which we depict informally as diagrams
\[ \xymatrix@R =40pt@C=20pt{ X_{0,0} \ar [dr] & & X_{1,1} \ar [dr] \ar [dl] & \cdots & X_{n-1,n-1} \ar [dr] \ar [dl] & & X_{n,n} \ar [dl] \\ & \cdots \ar [dr] & & \cdots \ar [dr] \ar [dl] & & \cdots \ar [dl] & \\ & & X_{0,n-1} \ar [dr] & & X_{1,n} \ar [dl] & & \\ & & & X_{0,n}. & & & \\ } \]