Western Marxism (both the train of thought called Western Marxism and Marxism in the West) is cultural. The eponymous founder of Marxism concentrated most of his effort on a critique of political economy. He showed that capitalism not only leads to cyclical crisis but that these cyclical crises over time lead to an existential one. In the Communist Manifesto this existential crises is described as having one of two results, either revolutionary reconstitution or common ruin. He showed that there is a class capable of positively resolving this crisis.
Despite many valiant attempts the question is why hasn’t the working class mission been completed? The answer is not economic, but cultural. Capital was written as a prognostication. In 1867 Marx was describing not capitalism as it was but as it could be expected to become. There was no according capitalist superstructure in 1867. There were no mass parties, nor universal suffrage. There was no mass education or popular culture. There were not even many of the countries that we recognise today.
The works of Antonio Gramsci are crucial. They are the beginnings of a theory of capitalist superstructure, capitalist culture, which organises, replicates and defends capitalist practice. The Prison Notebooks are an elaboration on the experiences both of the Biennio Rosso in Italy Soviet  Republic Italy 
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