Title: Actegories and Copowers with Application to Message Passing Semantics
Abstract: Reversible computing considers those computational operations which are reversible over a state space.
Generalized reversible computing aims to generalize the notion of reversible computing (closer to engineering) by considering a probability distribution over the initial set of states and considering reversibility of only those states with non-zero probability.
Not long ago, Michael P.Frank proposed a mathematical framework based on set theory for setting up the fundamental theorem generalized reversible computing relating (conditional) reversibility of an operation and entropy ejection by the operation. My colleague Clemence Chanavat and I realized that the framework has a categorical flavor.
In this talk, I aim to set up generalized reversible computing starting with partial Markov categories, especially, the Kleisli category of sub-distribution monads over partitioned sets. Once this is done, the fundamental theorem of generalized reversible computing can be set up as a functor of resource theories between the above mentioned Kleisli category into the indiscrete category of positive reals, [0,\infty].
This is a research in progress and would very much appreciate audience interaction!
