Your framing is essentially: take clusters of terms + their entailments, arrange them into a structured "space," and then look at the functors—structure-preserving maps—that carry one domain (political, economic, psychological, material) into another while preserving the relevant relations. That's a category-theoretic lens on social theory. Below I'll try to make that concrete, with the caveat that "functor" here is used somewhat loosely (real-world domains rarely form rigorous categories), but the heuristic is genuinely productive.
1. Setting up the "spaces"
Think of each domain as a category whose objects are states/positions and whose morphisms are transformations, dependencies, or implications between them.
Material domain (M): objects = stocks, flows, resources, means of production, bodies, infrastructure; morphisms = extraction, transformation, transport, depletion, degradation. Key relations: conservation, causal chaining, thermodynamic constraint.
Economic domain (E): objects = commodities, prices, capital, labor-power, firms, markets; morphisms = exchange, investment, accumulation, valuation. Key relations: equivalence (exchange-value), circulation, reproduction.
Political domain (P): objects = agents, offices, jurisdictions, coalitions, institutions; morphisms = authorization, coercion, legitimation, redistribution, boundary-drawing. Key relations: authority, sovereignty, inclusion/exclusion.
Psychological domain (Ψ): objects = desires, beliefs, affects, identities, capacities; morphisms = learning, repression, identification, motivation, habituation. Key relations: intentionality, valence, reinforcement.
The "constellation of terms" step matters: you don't get a functor until each domain's internal relations are pinned down, because a functor must preserve composition and identity—i.e., it must respect how implications chain.
2. Candidate functors between domains
Material → Economic (M → E): The classic candidate is a "valuation" functor: material objects map to commodities, material transformations map to production processes. It preserves composition only under specific conditions—when the material process is socially abstracted (Marx's real abstraction). Failure of functoriality is informative: externalities are precisely morphisms in M with no image in E (or with a distorted image). Ecological economics can be read as studying the obstruction to this functor.
Economic → Political (E → P): A "translation" functor maps economic power (capital concentration, market position) to political influence (lobbying capacity, agenda-setting). This is functorial only up to the "conversion rate" institutions impose—campaign finance law, corruption, franchise. Where composition fails (money → influence → policy doesn't compose the same way across jurisdictions), you've located institutional structure.
Psychological → Economic (Ψ → Ψ): Desire/valuation structures map onto demand curves and preference orderings—the revealed-preference functor. Behavioral economics documents where it fails to preserve composition (preference reversals, framing), i.e., where the functor is only lax/oplax.
Material → Psychological (M → Ψ): Affordances: material configurations map to possibilities-for-action perceived by agents (Gibson). This functor is selective—it forgets most material structure—which is exactly why misperception and ideology are possible.
Political → Psychological (P → Ψ): Interpellation/legitimation: institutional positions map to subject-positions and internalized norms (Althusser, Foucault, Bourdieu's habitus). Bourdieu is arguably the most explicitly functorial social theorist: field → habitus → practice, with field homomorphisms preserving capital structure.
The composite M → E → P → Ψ: This is the "base/superstructure" pipeline in its crudest form. The interesting theoretical work is showing where each leg is not a strict functor—where natural transformations (ideology, crisis, reform) mediate, and where the composite fails to commute with the direct M → Ψ affordance map. That non-commutation is a precise way to state "false consciousness" or "structural violence."
3. What the functorial framing buys you
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Compositionality: it forces you to say how a change in one domain propagates through chained implications, not just pairwise correlations.
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Obstruction theory: failures of functoriality (missing images, non-preserved composition) are diagnostic—they mark where a domain's terms don't cleanly translate, which is usually where the interesting social-theoretic action is (externalities, alienation, legitimacy crises).
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Adjunctions: pairs like "material affordance ⊣ perceived possibility" or "economic base ⊣ political superstructure" can be modeled as adjoint functors, capturing a weaker, directional preservation than isomorphism—often the right strength for social ontology.
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Natural transformations: comparative statics (institutional change, technological shift, ideological drift) become natural transformations between functors, letting you compare whole "regimes of translation" rather than single variables.
4. Honest caveats
Real domains aren't categories in the strict sense: objects are fuzzy, morphisms aren't closed under composition cleanly, and identity morphisms are theoretical fictions. So this is a modeling discipline, not a proof engine. Its value is (a) forcing explicit statement of relational structure before cross-domain claims, and (b) giving a vocabulary for partial and failing translations—which is most of what social theory actually studies.
If you want to push further, the natural next steps are: (i) specify one domain's category axioms concretely (economics is the most tractable—commodity categories, Sraffian production matrices as morphism composition); (ii) identify a specific natural transformation (e.g., a tax regime as a natural transformation between two E → P functors); and (iii) characterize the obstruction class for the M → E valuation functor as a formal stand-in for "externality." Want me to develop any one of those legs in more detail?