Displaying similar documents to “Lawvere's elementary theories and polyadic and cylindric algebras”

Initial normal covers in bi-Heyting toposes

Francis Borceux, Dominique Bourn, Peter Johnstone (2006)

Archivum Mathematicum

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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...