Is there a known definition of vector fields on a simplicial manifold?

For me, it seems natural that the definition should be something along the lines: Let $M_{\bullet}$ be a simplicial manifold with degeneracy maps $s_i: M_n \rightarrow M_{n+1}$ and face maps $\partial_i: M_{n+1} \rightarrow M_n$. A vector field on $M_{\bullet}$ is a vector field $X_n$ on each $M_n$ such that $X_n$ is $s_i$-related to $X_{n+1}$ plus some compatibility condition with $\partial_i$ (e.g. the Lie derivatives $\mathcal{L}_{X_n}$ commute with the Bott-Shulman differential $\delta = \sum (-1)^i \partial_i^*$).

However, I can't find any reference with a definition close to that.