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Morphisms as composeexpressible via as r0(f(α); ξ) = r(α; g(ξ)) for all α 2 A and ξ 2 X0: Morphisms compose via (f 0; g0)(f; g) = nnoindent(openf 0f; gg parenthesis0); whosedual pointsf associativity to the power , states of i s prime straightforward of comma an automaton g to the to power verify , or of . prime places When closing ofV a parenthesis= PetriSet the net open resulting depending parenthesis ordinary f on comma the g application closing parenthesis . = open parenthesiscategory f to of the ordinary power of Chu prime spaces f comma over ggK toand the power their of morphisms prime closing i s parenthesis comma whose associativity i s straightforward to verify period ..nnoindent Whendenoted V =ChMore Set u ( generallySet ;K); for the other obj ectsV a further and morphisms step enriches are the drawn homsets from to an make autonomous them objn ectsh f i l l ( symmetric the resulting ordinary category of ordinary Chu spaces over K and their morphisms i s nnoindentdenoted Chmonoidal u open parenthesis closed Set ) category comma K closing $ V parenthesis $ with tsemicolon ensor for product other V a $ further a n stepotimes enrichesb the homsets ,$ tensorunit to make them obj $I ects , $hline and internal hom Published on 2006 hyphen 1 2 hyphen 1 6 in the volume Chu spaces : theory and applications period Published on 2006 - 1 2 - 1 6 in the volume Chu spaces : theory and applications . n begin2000f Mathematicsa l i g n ∗g Subject Classification : 8 A 5 comma 8 A 70 comma 8 C 5 comma 1 8 B 1 5 comma 1 8 B 30 comma 1 8 D 1 5 comma 1 8 D 20 perioda n circ b . nendf2000a l i g Mathematics n ∗g Subject Classification : 8 A 5 , 8 A 70 , 8 C 5 , 1 8 B 1 5 , 1 8 B 30 , 1 8 D 1 5 , 1 8 D 20 . circlecopyrt-ccirclecopyrt Valeria− c deValeria Paiva de and Paiva Vaughan and Vaughan Pratt comma Pratt ,2006 2006 period .