Product preservation and stable units for reflections into idempotent subvarieties

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Aveiro, Portugal.

2 CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal.

10.29252/cgasa.13.1.1

Abstract

We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units if and only if it is simple and the above-mentioned condition holds.

Keywords

References

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Categories and General Algebraic Structures with Applications
Volume 13, Issue 1
July 2020
Pages 1-22

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