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We call a nitely complete category algebraically coherent if the change-of-base functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech,… (More)
We extend to semi-abelian categories the notion of characteristic subob-ject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of the classical properties of characteristic subgroups of a group hold in the general semi-abelian context, or in stronger ones.
Given a short exact sequence A → B → C in an abelian category, any morphism c: C ′ → C produces by pullback a new short exact sequence with the same kernel A. Dually, any morphism a: A → A ′ produces by pushout a new short exact sequence with the same cokernel C. If the base category is semi-abelian, the first construction still produces a short exact… (More)