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I have been looking at the very first example on this page of the documentation in Mathematica 11.3 (default installation options) and I get a different result:
LaunchKernels; Kernels; mykernel = First[Kernels]; a = 2; ParallelEvaluate[a === 2, mykernel]
whereas in the documentation it gives False.
Have there been any changes to parallel computing in Mathematica recently?