  In statistical inference, retrodiction is the act of inferring potential
causes in the past based on knowledge of the effects in the present and the
dynamics leading to the present. Retrodiction is applicable even when the
dynamics is not reversible, and it agrees with the reverse dynamics when it
exists, so that retrodiction may be viewed as an extension of inversion, i.e.,
time-reversal. Recently, an axiomatic definition of retrodiction has been made
in a way that is applicable to both classical and quantum probability using
ideas from category theory. Almost simultaneously, a framework for information
flow in in terms of semicartesian categories has been proposed in the setting
of categorical probability theory. Here, we formulate a general definition of
retrodiction to add to the information flow axioms in semicartesian categories,
thus providing an abstract framework for retrodiction beyond classical and
quantum probability theory. More precisely, we extend Bayesian inference, and
more generally Jeffrey's probability kinematics, to arbitrary semicartesian
categories.
