Abstract
Given a regular epimorphism f : X ↠ Y in an exact homological category C , and a pair ( U , V ) of kernel subobjects of X, we show that the quotient ( f ( U ) ∩ f ( V ) ) / f ( U ∩ V ) is always abelian. When C is nonpointed, i.e. only exact protomodular, the translation of the previous result is that, given any pair ( R , S ) of equivalence relations on X, the difference mapping δ : Y / f ( R ∩ S ) ↠ Y / ( f ( R ) ∩ f ( S ) ) has an abelian kernel relation. This last result actually holds true in any exact Mal'cev category. Setting Y = X / T , this result says that the difference mapping determined by the inclusion T ∪ ( R ∩ S ) ⩽ ( T ∪ R ) ∩ ( T ∪ S ) has an abelian kernel relation, which casts a new light on the congruence distributive property.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
