sdma

Use the SDMA decision matrix: coalgebra for evolving hidden state, linear logic for non-duplicable resources, category theory for cross-database migration, session types for multi-party protocols, and information theory for resilience analysis. The principle of minimal representation governs the final choice — pick the simplest formalism that faithfully captures the domain's structure.

Model each schema as a category with tables as objects and foreign keys as morphisms, then apply the three adjoint migration functors. Use Δ (pullback) for reformatting and views, Σ (left pushforward) for merging datasets, and Π (right pushforward) for constraint enforcement across schema boundaries.

An olog (ontology log) is a categorical knowledge representation where objects are singular indefinite noun phrases, morphisms are functional relationships, and facts are commutative diagrams. Use ologs for domain modeling and knowledge representation where business rules must be verifiable as path equations.

Use coalgebra when the problem involves hidden internal state, potentially infinite behavior like streams or protocols, or when behavioral equivalence matters more than structural identity. Use algebra when constructing finite data structures like lists, trees, and algebraic data types.

Compute the Structural Entropy Index of a Community (SEIC), defined as the Shannon entropy of the degree distribution divided by log₂ of the community size. Values near 1 indicate decentralized resilient structure, while values near 0 indicate hub-dominated fragility; compare against Maslov-Sneppen null models to distinguish deliberate design from random growth.

Ologs only express simple path equalities and cannot handle quantified logic like 'for all employees there exists a manager.' For first-order constraints use hyperdoctrines with quantifiers as adjoints, and for provability reasoning use triposes over the Effective Topos.