Is there a commonly used notation for flipped composition?

Question

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.

$$ \require{AMScd} \begin{CD} X @>{f \circ g}>> Y \\ @VVgV @AAfA \\ g(X) @>{id}>> g(X)\end{CD} $$

Answer 1

Computer scientists may write g ; f for f ∘ g

See:Function composition - Alternative notations

Answer 2

I personally use the notation $f$»$g$, which is inspired by the F# operator >>. Perhaps you like that too, although it isn't established by any means.

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In LaTeX it should be \text{\guillemotright} with:

\usepackage[T1]{fontenc} 

and

 \usepackage{amsmath}

Answer 3

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.