论文标题
量子梳子的光学元件
Coend Optics for Quantum Combs
论文作者
论文摘要
我们比较了一种定义1个类别的1个类别的可能方法，即第一个作为coend光学元件，而第二次延伸作为商品作为商在低阶图上的操作行为作为商。我们表明，对象有一个完整的和射形的物体函子对扩展定义的强度定义，并给出了一些足够的条件，使该函子成为类别的同构。我们还展示了如何扩展1-COMB的构造，以产生N-COMB的多类，其结果相似，何时这些多类是等效的。扩展定义在量子梳的研究中特别感兴趣，我们希望这项工作可能会对在量子理论中对这些结构进行建模的光学的使用产生进一步的兴趣。
We compare two possible ways of defining a category of 1-combs, the first intensionally as coend optics and the second extensionally as a quotient by the operational behaviour of 1-combs on lower-order maps. We show that there is a full and bijective on objects functor quotienting the intensional definition to the extensional one and give some sufficient conditions for this functor to be an isomorphism of categories. We also show how the constructions for 1-combs can be extended to produce polycategories of n-combs with similar results about when these polycategories are equivalent. The extensional definition is of particular interest in the study of quantum combs and we hope this work might produce further interest in the usage of optics for modelling these structures in quantum theory.
