Lambdacus
Articles on the mathematical foundations of enterprise security and data architecture. We formalize access control, data lineage, and platform structure as categorical constructions (toposes, monads, adjunctions) and show how concrete systems arise as their representations.
Articles
- Lambdacus: The Framework The foundations of categorified security.
- Component 1: The Schema The shape of the domain as a small category.
- Component 2: The Presheaf Data as a contravariant functor on the schema.
- Component 3: The Presheaf Category The state space as an elementary topos.
- Component 4: The Edit Monad Composable state transitions as a monad on the topos.
- Component 5: The Grothendieck Topology Security as a topological structure on the schema.
- Component 6: The Lineage Category Provenance as a free category on a directed acyclic graph.