When defining maps from higher to lower dimensional spaces explicitly, say from $\mathbb{R}^{n+1}$ to $\mathbb{R}^{n}$, one often sees something like this: $$(x_0,...,x_n)\mapsto(x_0,...,\hat{x}_i,...,x_n),$$ where the hat means that $x_i$ is omitted. Is there a similar notation for the opposite, i.e. insertion of an additional coordinate (like e.g. $\check{x}_i$)?
I'd be gateful for advice.
I've most often seen the notation
$$ (x_1, \ldots, x_n) \mapsto (x_1, \ldots, x_i, y, x_{i+1},\ldots, x_n)$$
I hope this helps ^_^