On Operations with Binders and Operations with Equations

Abstract

We compare the category theoretic semantics for binding signatures by Power and Tanaka with the abstract approach to universal algebra by Hyland. It
is striking to see that two different ideas turn out to be so similar. We especially note that both approaches rely heavily on considering a monoid in the monoidal structure induced by a 0-cell in the Kleisli bicategory generated by a pseudo-distributive law of pseudo-monads. We further explain the implications the discovery of those similarities have by considering constructions that were only used in either of the two bodies of work.

Date of Award	22 Jul 2020
Original language	English
Awarding Institution	University of Bath
Supervisor	Anthony Power (Supervisor) & Alessio Guglielmi (Supervisor)