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Generalizing Substitution

Tarmo Uustalu (2010)

RAIRO - Theoretical Informatics and Applications

It is well known that, given an endofunctor H on a category C , the initial (A+H-)-algebras (if existing), i.e. , the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete...

Hopf-Galois extensions for monoidal Hom-Hopf algebras

Yuanyuan Chen, Liangyun Zhang (2016)

Colloquium Mathematicae

Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.

How algebraic is algebra?

Adámek, Jiří, Lawvere, F.W., Rosický, Jiří (2001)

Theory and Applications of Categories [electronic only]

Hu's Primal Algebra Theorem revisited

Hans-Eberhard Porst (2000)

Commentationes Mathematicae Universitatis Carolinae

It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.

Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.

Integrating observational and computational features in the specification of state-based, dynamical systems

Corina Cîrstea (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system...

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