[12/03/24] Partner Event - 2-Dimensional Monads and Concurrency

About the event

Abstract:

This talk is about 2-dimensional categories in semantics. A number of recent semantic models are defined as bicategories (e.g. games, spans, profunctors), and many traditional models can be regarded as 2-categorical (e.g. domain theory, or models for non-determinism), so it is important to develop this theory. 

This talk is specifically about 2-dimensional monads. I will first give some new results that generalize the traditional theory of strong and commutative monads to a 2-categorical setting. These results can be used to reason about the sequencing of effectful programs, even if the semantic model is not a strict category. 

Then, I will introduce "concurrent" 2-monads, which can be used to reason about programs composed either sequentially or in parallel. Concurrent 2-monads sit strictly between strong and commutative 2-monads, but this level is invisible in the 1-dimensional setting, because it requires non-invertible 2-cells. 

This is joint work with Philip Saville.

Meeting Link

Meeting ID 96318912

Passcode 542647

Speaker Bio:

Hugo is a postdoctoral research fellow at the LIPN in Paris. His research is about the theory of programming languages, especially denotational semantics, game semantics, and categorical foundations. He is also interested in statistical probabilistic programming. Before moving to Paris, Hugo spent many years in the UK, first as a PhD student with Glynn Winskel in Cambridge, and then as a postdoc in Oxford with Sam Staton and Luke Ong.