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Divisibility in categories of a class which includes the category of binary relations

Published online by Cambridge University Press:  18 May 2009

D. G. Fitz-Gerald
D. G. Fitz-Gerald
Affiliation:
University of QueenslandSt. Lucia, Queensland
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Green's relations are essential for “co-ordinatizing” semigroups. Jacqueline Klasa, in applying cognate ideas to categories [4, 5], has shown that divisibility in suitably-behaved categories may be described in terms of subobjects and quotients.

Here it is shown that adjoint functors which are onto objects preserve divisibility (in a certain sense). The inclusion functor of the category of sets into the category R of binary relations is such a functor. A slight modification of its right adjoint allows the representation of R as a full subcategory in a category CSL of complete semilattice morphisms.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 1 , January 1976 , pp. 22 - 30
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

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