This question is part category theory and part philosophy.
Lawvere claims that a Hegelian dialectic is an adjunction between idempotent (co)monads. The dialectical materialism of Marx and Engels is generally considered to be a Hegelian dialectic. Engels states that a material dialectic must satisfy:
- The law of the unity and conflict of opposites
- The law of the passage of quantitative changes into qualitative changes
- The law of the negation of the negation
This seems a lot like an adjunction because the first condition would be a Galois connection, and the second is the syntax/semantics adjunction. Not so sure about the third law.
This leads to a funny question. Marxist economic theory studies the material dialectic between class struggle and material condition. Are there categories characterising the progression of class dynamics and the material reality which form idempotent, adjoint monads?
For example, is class a poset? We know that adjunctions between posets are idempotent, so this seems possible.
Lawvere, F. William, Some thoughts on the future of category theory, Category theory, Proc. Int. Conf., Como/Italy 1990, Lect. Notes Math. 1488, 1-13 (1991). ZBL0779.18001.