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.



Vector fields on a simplicial manifold.
How about this? Apply the tangent functor $T$ to $M\_\bullet$ to get a new simplicial manifold $TM\_\bullet,$ that is take the composite


$$\Delta^{op} \stackrel{M\_\bullet}{\longrightarrow} Mfd \stackrel{T}{\longrightarrow} VectBun \to Mfd,$$ where the last functor is the forgetful functor. There is an obvious map $\pi\_\bullet:TM\_\bullet \to M\_\bullet.$ Say a vectorfield on $M\_\bullet$ is a section $X\_\bullet$ of $\pi\_\bullet$ in the category of simplicial manifolds.


