Abstract
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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Adámek, J., Rosický, J. On Pure Quotients and Pure Subobjects. Czechoslovak Mathematical Journal 54, 623–636 (2004). https://doi.org/10.1007/s10587-004-6413-9
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DOI: https://doi.org/10.1007/s10587-004-6413-9