What problem does it solve? Engineers designing protocols, state machines, and data schemas often lack a shared formal vocabulary to reason about correctness, equivalence, and composition, leading to ad-hoc verification and missed structural errors. ## Core Features & Use Cases - Categorical Foundations: Defines symmetric monoidal categories, closed and compact closed structures, and coherence axioms (pentagon, hexagon, zig-zag identities) for reasoning about composition. - Rosetta Stone Correspondences: Maps physics, topology, logic, and computation onto one algebraic structure, including Curry-Howard (types as propositions) and linear type theory for resource discipline. - Algebra vs. Coalgebra Guidance: Explains bisimulation for behavioral equivalence of state machines and protocols, plus database schemas as categories with adjoint data migrations (Kan extensions). - Use Case: When verifying that two protocol implementations are behaviorally equivalent, use this skill to frame the question as a bisimulation check rather than structural comparison. ## Quick Start Ask the agent to load the formal-foundations skill and explain whether two state machines are equivalent using bisimulation.
