On Pure Quotients and Pure Subobjects

Author: Adámek J.   Rosický J.  

Publisher: Springer Publishing Company

ISSN: 0011-4642

Source: Czechoslovak Mathematical Journal, Vol.54, Iss.3, 2004-09, pp. : 623-636

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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.