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A generalized minimal realization theory of machines in a category.

Antonio Bahamonde (1983)

Stochastica

This paper presents a generalized minimal realization theory of machines in a category which contains the Kleiski case. The minimal realization is the cheapest realization for a given cost functor. The final reachable realization of Arbib and Manes ([5]) and the minimal state approach for nondeterministic machines are included here.

A logic of orthogonality

Jiří Adámek, Michel Hébert, Lurdes Sousa (2006)

Archivum Mathematicum

A logic of orthogonality characterizes all “orthogonality consequences" of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of morphisms such that all members except a set are regular epimorphisms and (b) for all classes Σ , without...

A Maschke type theorem for relative Hom-Hopf modules

Shuangjian Guo, Xiu-Li Chen (2014)

Czechoslovak Mathematical Journal

Let ( H , α ) be a monoidal Hom-Hopf algebra and ( A , β ) a right ( H , α ) -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor F from the category of relative Hom-Hopf modules to the category of right ( A , β ) -Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the ( H , α ) -coaction to be separable. This leads to a generalized...

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