Some Categorical Observations on State Effects

  • Soichiro Fujii


  • Aug. 28, 2016, 10:25 - 12:30


From the outset, state effects have been the leading examples in the algebraic approach to computational effects. Indeed, the approach itself started from the recognition that the global state admits a computationally natural presentation in terms of operations and equations, and the mysterious nature of the local state has attracted much attention and stimulated considerable research in the field.

In this talk, I attempt to shed new light on both the global and local states. First, I explain that the now standard presentation of the global state monad on Set (in terms of the update and lookup operations) is a particular instance of a much more general phenomenon, whose first appearance essentially dates back to Lawvere’s thesis. Second, I present a decomposition of the local state monad on [Inj, Set] based on the category of elements constructed from a presheaf of variable states.