For any natural number $n$, let $i_{n},j_{n}:X_{n}\rightarrow X_{n+1}$ be a pair of monomorphisms of simplcial sets.

Define $$X=colim_{n}\{\cdots X_{n}\rightarrow_{i_{n}} X_{n+1}\cdots \} $$ and $$Y=colim_{n}\{\cdots X_{n}\rightarrow_{j_{n}} X_{n+1}\cdots \}$$

Question: I'm looking for an example where $X$ is not isomorphic to $Y$ as a simplicial set.

For any natural number $n$, let $i_{n},j_{n}:X_{n}\rightarrow X_{n+1}$ be a pair of monomorphisms of simplcial sets.

Define $$X=\operatorname*{colim}_n \{\cdots X_n \rightarrow_{i_n} X_{n+1}\cdots \} $$ and $$Y=\operatorname*{colim}_n \{\cdots X_n \rightarrow_{j_n} X_{n+1}\cdots \}$$

Question: I'm looking for an example where $X$ is not isomorphic to $Y$ as a simplicial set.