Exercise 7.2.8.11. Let $\operatorname{{\bf \Delta }}_{\leq 1}$ denote the full subcategory of $\operatorname{{\bf \Delta }}$ spanned by the objects $[0]$ and $[1]$, which we depict informally as a diagram
\[ \xymatrix@R =50pt@C=50pt{ [0] \ar@ <.8ex>[r] \ar@ <-.8ex>[r] & [1]. \ar [l] } \]
Show that:
The opposite category $\operatorname{{\bf \Delta }}_{\leq 1}^{\operatorname{op}}$ satisfies condition $(\ast )$ of Warning 7.2.8.2 (that is, it is a sifted category in the sense of [MR1815045]).
The simplicial set $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\leq 1}^{\operatorname{op}})$ is not sifted.