This question is part of the theory of categories and philosophy.
Lawvere asserts that a Hegelian dialectic is an adjunction between idempotent (co) monads. The dialectical materialism of Marx and Engels is generally considered a Hegelian dialectic.
Engels states that one material dialectic must satisfy:
- The law of unity and the conflict of opposites
- The law of passage from quantitative changes to qualitative changes
- The law of negation of negation
This is very similar to an addition because the first condition would be a Galois connection and the second is a syntactic / semantic addition.
Not so sure of the third law.
This leads to a fun question.
Marxist economic theory studies the material dialectic between class struggle and material condition.
Are there categories characterizing the progression of class dynamics and material reality that form idempotent adjunct monads?
For example, does the class form a category of posets?
Lawvere, F. WilliamSome reflections on the future of the theory of categories, Theory of categories, Proc. Int. Conf., Como / Italy 1990, Lect. Notes Math. 1488, 1-13 (1991). ZBL0779.18001.