The concept of a coupled quantales is introduced as a non-commutative extension of the concept of biframes. Also an approach to non-commutative bitopology is studied. Then an adjunction between the category of coupled quantales and the category of biquantum spaces is established.

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The concept of coupled semi-quantales is introduced. An adjunction between the category of coupled semi-quantales and the category of lattice-valued biquasi-topological spaces is established. The topological and the lattice-theoretic concepts of regularity and compactness are extended to both lattice-valued biquasitopological spaces and coupled semi-quantales, respectively. Some relations among these axioms are established.