## Parametrized Fixed Points and Their Applications To Session Types

Ryan Kavanagh Parametrized Fixed Points and Their Applications To Session Types Electronic Notes in Theoretical Computer Science 352 October 2020 The 36th Mathematical Foundations of Programming Semantics Conference, 2020 149-172 10.1016/j.entcs.2020.09.008
Parametrized fixed points are of particular interest to denotational semantics and are often given by “dagger operations”. Dagger operations that satisfy the Conway identities are particularly useful, because these identities imply a large class of identities used in semantic reasoning. We generalize existing techniques to define dagger operations on $$\omega$$-categories and on $$\textbf{O}$$-categories. These operations enjoy a 2-categorical structure that implies the Conway identities. We illustrate these operators by considering applications to the semantics of session-typed languages.