O-categories generalize categories of domains to provide just the structure required to compute fixed points of locally continuous functors. Parametrized fixed points are of particular interest to denotational semantics and are often given by "dagger operations". We generalize existing techniques to define a functorial dagger operation on locally continuous functors between O-categories. We show that this dagger operation satisfies the Conway identities, a collection of identities used to axiomatize iteration theories. We study the behaviour of this dagger operation on natural transformations and consider applications to semantics of session-typed languages.

中文翻译：

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O 类别上的参数化不动点和会话类型的应用

O-categories 将域的类别概括为仅提供计算局部连续函子的不动点所需的结构。参数化不动点对指称语义特别感兴趣，通常由“匕首操作”给出。我们推广现有技术以在 O 类别之间的局部连续函子上定义函子匕首操作。我们证明了这个匕首操作满足康威恒等式，这是一组用于公理化迭代理论的恒等式。我们研究了这种 dagger 操作对自然转换的行为，并考虑了对会话类型语言语义的应用。