Relational Foundations For Functorial Data Migration

Understand

We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations.

• Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories.
• A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst.
• A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $\Sigma_F:S$-inst$\to T$-inst, $\Pi_F: S$-inst $\to T$-inst, and $\Delta_F:T$-inst $\to S$-inst.