Cartesian monoid

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A Cartesian monoid is a monoid, with additional structure of pairing and projection operators. It was first formulated by Dana Scott and Joachim Lambek independently.^[1]

A Cartesian monoid is a structure with signature ${\ estilo de visualización \ langle *, e, (-,-), L, R \ rangle}$ where ${\ estilo de visualización *}$ and ${\ estilo de visualización (-,-)}$ are binary operations, ${\ estilo de visualización L, R}$, and ${\ estilo de visualización e}$ are constants satisfying the following axioms for all ${\ estilo de visualización x, y, z}$ in its universe:

The interpretation is that ${\ estilo de visualización L}$ and ${\ estilo de visualización R}$ are left and right projection functions respectively for the pairing function ${\ estilo de visualización (-,-)}$.

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