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On pure quotients and pure subobjects
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 623-636
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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.
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.
Classification : 18A99, 18E99
Keywords: pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category 
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Adámek, J.; Rosický, J. On pure quotients and pure subobjects. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 623-636. http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a6/

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