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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.

Initial normal covers in bi-Heyting toposes

Francis Borceux, Dominique Bourn, Peter Johnstone (2006)

Archivum Mathematicum

The dual of the category of pointed objects of a topos is semi-abelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes, actions are representable provided the topos admits an essential Boolean covering. This contains the...

Injective models of G -disconnected simplicial sets

Marek Golasiński (1997)

Annales de l'institut Fourier

We generalize the results by G.V. Triantafillou and B. Fine on G -disconnected simplicial sets. An existence of an injective minimal model for a complete 𝕀 -algebra is presented, for any E I -category 𝕀 . We then make use of the E I -category 𝒪 ( G , X ) associated with a G -simplicial set X to apply these results to the category of G -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent G -simplicial set by means of its injective minimal model.

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