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Keywords:
pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category
pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category
Summary:
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.
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