FCDB (Functorial-Categorical Database): A Compositional Framework for Information Preservation and Anti-Commutativity Reduction

TL;DR

The paper introduces FCDB, a categorical framework for databases that preserves information and reduces non-commutativity, enabling better integrity and semantics without data loss.

Contribution

It proposes a novel functorial-categorical model for databases that maintains information integrity and handles non-commutativity through a minimal kernel and layered projections.

Findings

Preserves content invariance and ownership integrity.

Ensures commutativity in categorical limits.

Supports empirical validation without losing semantic information.

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.