  We introduce structured active inference, a large generalization and
formalization of active inference using the tools of categorical systems
theory. We cast generative models formally as systems "on an interface", with
the latter being a compositional abstraction of the usual notion of Markov
blanket; agents are then 'controllers' for their generative models, formally
dual to them. This opens the active inference landscape to new horizons, such
as: agents with structured interfaces (e.g. with 'mode-dependence', or that
interact with computer APIs); agents that can manage other agents; and
'meta-agents', that use active inference to change their (internal or external)
structure. With structured interfaces, we also gain structured ('typed')
policies, which are amenable to formal verification, an important step towards
safe artificial agents. Moreover, we can make use of categorical logic to
describe express agents' goals as formal predicates, whose satisfaction may be
dependent on the interaction context. This points towards powerful
compositional tools to constrain and control self-organizing ensembles of
agents.
