Is there a commonly used notation for flipped composition? We have $ (f \circ g) = x \mapsto f(g(x)) $ however since I read left to write it always seems backwards to me.  Is there a symbol like $ ( g \ggg f) = x \mapsto f(g(x)) $.
It is especially grating in situations like.
$$ 
\require{AMScd} \begin{CD} X @>{f \circ g}>> Y \\ 
@VVgV @AAfA \\
g(X) @>{id}>> g(X)\end{CD}
$$

Some math books (especially abstract algebra) may write composition in the reverse order: $\sigma\tau$ means: first $\sigma$ then $\tau$.  For notation they write
$$
  x^{\sigma \tau} = \big(x^\sigma\big)^\tau
$$
For example, this may be seen with field automorphisms.
