Protolocalisations of exact Mal'cev categories.
When is a cogenerator in a topos ?
Limites enrichies et existence de -foncteur adjoint
Algebraic localizations and elementary toposes
Complétion universelle des catégories
Skew -sets coincide with -posets
A theory of enriched sheaves
Cauchy completion in category theory
Sheaves on a quantale
Structure des topologies d'un topos
On primeness and maximality of filters
De Morgan's and strong De Morgan's laws in a topos of shaves
Initial normal covers in bi-Heyting toposes
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...
Foreword
Internal object actions
We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.
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