2-Dimensional Monads and Concurrency

Hugo Paquet
LIPN, Université Sorbonne Paris Nord

Date(s) : 22/02/2024   iCal
11 h 00 min - 12 h 30 min

This talk is about 2-dimensional categories (2-categories or bicategories) in semantics. A number of recent denotational models are defined as bicategories (typically based on games, spans, or profunctors) and many traditional models are already 2-categorical (e.g. categories of domains, or models for non-determinism), so it is important to develop this theory.

This talk is about 2-dimensional monads (2-monads or pseudomonads). First I will give some new results that extend the traditional 1-dimensional theory of strong and commutative monads. These results can be used to reason about the sequencing of effectful programs in 2-dimensional semantic models.

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. To illustrate and motivate these definitions I will use the double-negation monad in concurrent games.

Site Sud, Luminy, TPR2, Amphithéâtre Herbrand 130-134 (1er étage)


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