Displaying similar documents to “On the representability of actions in a semi-abelian category.”

Moore categories.

Rodelo, Diana (2004)

Theory and Applications of Categories [electronic only]

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Enlargements of categories.

Brünjes, Lars, Serpé, Christian (2005)

Theory and Applications of Categories [electronic only]

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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...

On pure quotients and pure subobjects

Jiří Adámek, Jiří Rosický (2004)

Czechoslovak Mathematical Journal

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In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.