acsets-algebraic-databases

ACSets (Attributed C-Sets) represent relational structures as functors using category theory, enabling you to define schemas with objects and morphisms, then query them with composable map, filter, and fold operations on in-memory data.

ACSets provide formal, functorial representations of schemas using category theory, offering structured composition and extension over standard SQL—suited for schema-driven modeling where attribute attachment and graph navigation matter more than disk persistence.

Yes. ACSets support vertex and edge sets with attached attributes, functional map, filter, and fold interfaces, and open composition interfaces, making them suitable for both graph traversal and tabular attribute operations.

ACSets work with Catlab and AlgebraicJulia tooling through open integration interfaces, enabling composition with other category-theoretic workflows including GF(3) conservation integration for Music Topos applications.

Define a small category schema with objects (vertices, edges) and morphisms (source, target mappings). This categorical foundation lifts to an ACSet type for querying and attribute management.

Use ACSets when you need principled schema management, composable queries on graph-with-attributes structures, or formal algebraic semantics—particularly for music theory, knowledge graphs, or systems requiring categorical extension.