equivalent 1-simplices

Let \(X\) be a simplicial set and \(f,g \in X([1])\) be \(1\)-simplices from \(x\) to \(y\) Then \(f,g\) are equivalent, if there exists a 2-simplex

\begin{align*} \sigma: \Delta^2 \rightarrow X \end{align*}

satisfying following conditions

1. \(\sigma_{v \Delta^{[0,1]}} = f\)
2. \(\sigma_{v \Delta^{[0,2]}} = g\)
3. \(\sigma_{v \Delta^{[1,2]}} = \mathrm{id}_{y}\)