Can we use AlgebraicMultigrid.jl with a matrix-free operator?

[amontoison]

I would like to use the preconditioner in this package with solvers in Krylov.jl.
The operator that I would like to use only supports mul!(y, A, x).

[termi-official]

I am not aware of any AMG technique which is able to handle operators which do not come in an explicit form. The bottleneck is that in AMG solvers you typically analyze the graph of $A$ to derive a hierarchy of smaller matrices through graph coarsening algorithms.