We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing that they inherit significant categorical structure from the free cornering, including that they form monoidal double categories. We also establish some elementary properties of the novel structure they contain. Further, we give a model of the free cornering in terms of strong functors and strong natural transformations, inspired by the literature on computational effects.

翻译：我们扩展了对称幺半范畴的自由角化（一种并发交互的双范畴模型），以支持分支通信协议和迭代通信协议。通过证明这些构造继承了自由角化中的重要范畴结构（包括形成幺半双范畴），我们验证了其有效性。同时，我们建立了其中包含的新型结构的一些基本性质。此外，受计算效应文献启发，我们基于强函子与强自然变换给出了自由角化的一种模型。