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A morphism is an emulation if: ∀ v ^ ∈ ℝ + S ^ F v ^ ∘ m S = F ^ v ^ ∘ m S (Definition: Emulation) This says that the derivatives of the two systems are related by m S. In particular, the derivatives coincide when the initial states coincide under m S, guaranteeing by determinism that whole trajectories coincide.
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