Product preservation and stable units for reflections into idempotent subvarieties

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:

Semi-left-exactness , stable units , simple reflection , preservation of finite products , varieties of universal algebras , idempotent