I'm currently working with (graded)supermanifolds with applications to another fields. My main example is $T[1]M$ the shifted tangent bundle of a manifold. I understand how gluing functions work for regular tangent bundle $TM$, but I dont understand how they work for shifted tangent bundle, I know how to build morphisms from $\mathbb{R}^{p|q}$ to $\mathbb{R}^{p|q}$. Suppose I have smooth manifold M, I have atlas $\{\{ U_i\},\varphi_i\}$ and smooth functions $C^{\infty}(M)$, then I work with $T[1]M$ as a supermanifold with functions $\Omega(M,\mathbb{R})$, so my questions is how does the coordinate change works for $T[1]M$.
any hints would be appreciated.
