Speaker: Tarmo Uustalu, Reykjavik University & Tallinn University of Technology
Time: Thursday 1 October 2026, 10:30am
Place: 1B36, ENS Paris-Saclay
Abstract: Concurrent monads, due to Rivas and Jaskelioff, are a specialization of monads, namely a relaxation of lax monoidal monads (commutative monads) in ordered category theory. For the application in categorical semantics of functional programming languages, they are an abstraction of notions of effectful computation that are composable not only sequentially but also in parallel. Both the sequential and parallel compositions are unital and associative; more significantly, they are interrelated by interchange inequations. Concurrent monads categorify the ordered-algebraic concept of concurrent monoids from concurrency theory, going back to Grabowski and Gischer.
I will motivate and introduce this elegant abstraction, which treats parallel composition on a par with sequential composition, present some theory and show some examples from programming language semantics and concurrency theory.