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Products and tensor products are linked by a universal property. Imposing theinvariance of the laws of Nature under tensor composition along with Leibnizidentity determines quantum and classical mechanics algebraic structure throughthe interplay between products, coproducts, and the tensor product. Violationsof Bell's inequalities distinguishes quantum from classical mechanics.

Derivation of Quantum Mechanics algebraic structure from invariance of the laws of Nature under system composition and Leibniz identity