We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin's system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization without commuting conversions. Despite this simplicity, the calculus is shown to be sound and complete for category-theoretic models given by *-autonomous categories with linear exponential comonads.
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