Zeinab Galal (LIP6, Sorbonne Université), Bidimensional fixpoint operators



Fixpoint operators are tools to reason on recursive programs and infinite data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. An important result by Plotkin and Simpson in this area states that provided some conditions on bifree algebras are satisfied, we obtain the existence of a unique uniform fixpoint operator. This theorem allows to recover the well-known examples of the category Cppo (complete pointed partial orders and continuous functions) in domain theory and the relational model in linear logic. In this talk, I will present a categorification of this result where the 2-dimensional framework allows to study the coherences associated to the reductions of λ-calculi with fixpoints i.e. the equations satisfied by the program computations steps.