AI 中文总结
本文借助丰富范畴论，将非单位算子系统与矩阵代数范畴上的模建立范畴等价，并推广了相关分离、表示与扩张定理，部分恢复了算子系统的经典结果。
AI 中文摘要
算子系统类似于环上的模，其中标量乘法的角色由完全正映射的作用承担。利用丰富范畴论，我们将这一类比转化为精确的范畴等价：一类非单位算子系统范畴与以正则序巴拿赫空间为丰富的矩阵代数范畴上的左模范畴等价；若改用右模，则得到与一类非单位对偶算子系统范畴的等价。我们还建立了丰富范畴论中模的一般分离、表示与扩张定理，将其应用于非单位算子系统，可部分恢复算子系统对应的经典定理。
英文摘要
An operator system is similar to a module over a ring, with the role of scalar multiplication played by the action of completely positive maps. Using enriched category theory, we make this analogy into a precise categorical equivalence, namely between a certain category of nonunital operator systems and a certain category of left modules over the category of matrix algebras enriched over regularly ordered Banach spaces. Using right modules instead yields an equivalence with a certain category of nonunital dual operator systems. We also develop general separation, representation and extension theorems for modules in enriched category theory. Specializing these to our nonunital operator systems recovers results which partly recover the corresponding classical theorems for operator systems.
