Woke is a recently popular word, politically correctly interpreted as meaning leftist politically “awake” or “aware”.
Leftist Wikipedia claims that the word is of Black origin, therefore implied to be more politically correct, despite the word long being a simple past tense of “wake”, derived from a Germanic word.
Leftist supremacism is an ideology based on the belief that (certain) leftists are a superior group and therefore should control or rule other groups.
Communism, especially its common Marxist-Leninist variant, includes concepts such as “dictatorship of the proletariat” and “vanguard party” that in effect mean that Communists should rule over non-Communists, even if this is against the wishes of the majority of the population. Demands for a worldwide Communist revolution mean that Communism should be spread by force and conquer the whole world.
Social anarchism by definition, in theory, excludes anyone ruling over anyone, but when social anarchists briefly controlled some territory during the Spanish Civil War, they committed large-scale violence against suspected opponents.
The Frankfurt School and Critical Theory – Cultural Marxism