## A unified minimal realization theory, with duality, for machines in a hyperdoctrine: announcement of results : technical report |

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### Contents

Introduction 1 A Fundamental Example | 1 |

Hyperdoctrines | 8 |

A Reformulation of Machine Theory | 10 |

3 other sections not shown

### Common terms and phrases

adjoint to inclusion adjoint yu algebra automata algebraic structure arbitrary recursive computations assigns automata and system automata theory Beh(u behaviour scheme cartesian closed category category of right category of sets category P(X closed monoidal category computations as behaviours construction coordinatized action coordinatized machine corresponding define a morphism denote dual equational theory forgetful functor free monoid ft(I functor from right graph higher order logic hyperdoctrine cat input monoid interpreted Kalman duality Lawvere left adjoint linear systems Mach(u machine theory machines in cat machines with algebraic machines with restricted minimal realization theories modules monadic morphism h natural coordinatization natural number numbers under addition Obs(u ordinary machines P(Xop product preserving functors Rch(u reachability and observability recursive function reduced realization restricted input right action right adjoint right K[z]-module sequential machines small category sub f subaction subobject tensor product topos type of machine unifies universal quantification vector space X-actions to sets