Relative weak injectivity of operator system pairs

The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg 11] proved that the C^?${\mathrm{C}}^{?}$-algebra C^?(_F∞)${\mathrm{C}}^{?}({\mathbb{F}}_{\infty })$ of the free group _F∞${\mathbb{F}}_{\infty }$ on countably many generators characterises relative weak injectivity for pairs of C^?${\mathrm{C}}^{?}$-algebras by means of the maximal tensor product. One of the main results of this paper shows that C^?(_F∞)${\mathrm{C}}^{?}({\mathbb{F}}_{\infty })$ also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products  and .