Editing Markov decision process (section)

===Category theoretic interpretation===
Other than the rewards, a Markov decision process <math>(S,A,P)</math> can be understood in terms of [[Category theory]]. Namely, let <math>\mathcal{A}</math> denote the [[free monoid]] with generating set ''A''. Let '''Dist''' denote the [[Kleisli category]] of the [http://ncatlab.org/nlab/show/Giry+monad Giry monad]. Then a functor <math>\mathcal{A}\to\mathbf{Dist}</math> encodes both the set ''S'' of states and the probability function ''P''.

In this way, Markov decision processes could be generalized from monoids (categories with one object) to arbitrary categories. One can call the result <math>(\mathcal{C}, F:\mathcal{C}\to \mathbf{Dist})</math> a ''context-dependent Markov decision process'', because moving from one object to another in <math>\mathcal{C}</math> changes the set of available actions and the set of possible states.{{Citation needed|reason=No reference is provided|date=December 2020}}