That really depends on your definition of ‘left-wing’.

Because I would argue that ‘left-wing’ is not only a descriptor for a political agenda. It also that includes economic issues. To me an economic system is pretty important part of a political system.

For instance, I would say that ‘free market communism’ doesn’t exist. I would also say that ‘authoritarian communism’ doesn’t exist. To me authoritarian and socialistic ideas are not compatible, because power is in the hands of an elite, and control mechanisms of that power were never strong enough. Control mechanisms of democracies worked generally better, but democracies also need to be properly defended and maintained.