FCDB (Functorial-Categorical Database): A Compositional Framework for Information Preservation and Anti-Commutativity Reduction
Jun Kawasaki
TL;DR
Conventional DBs trade information for local consistency, prompting the need for information-preserving architectures. The paper introduces the Functorial-Categorical Database (Enishi), a layered framework that combines Graph, CAS, Capability, and Ownership via a functorial-categorical structure to preserve data while reducing anti-commutativity. Key contributions include the kernel F_core = Own o Cap o CAS, a Complete Preserving Family of projections, an adjoint double-category formulation, and empirical validation showing near-commutative execution and strong performance. The approach enables semantic-rich, history-aware data management without sacrificing safety, and provides a concrete path for reproducible evaluation and future integration with existing data systems.
Abstract
Conventional database architectures often secure local consistency by discarding information, entangling correctness with loss. We introduce the Functorial-Categorical Database (FCDb), which models data operations as morphisms in a layered functor category and establishes a Complete Preserving Family (CPF) of projections spanning content invariance (CAS), capability, and ownership, with optional observational projections for local order (B+Tree), temporal history (append-only/LSM), and adjacency (Graph). We identify a minimal kernel (F_core = Own o Cap o CAS) that preserves information and collapses non-commutativity to the ethical grant/revoke boundary. Under adjoint lifts and a fibred structure, operational pairs commute in the categorical limit while ownership integrity and capability constraints are maintained. The framework connects to information geometry via projection interpretations and supports empirical validation without discarding semantic, temporal, or relational entropy.