Abstract
We give a simple proof of a wreath product decomposition for locally ℛ-trivial finite categories. As immediate consequences we obtain two classic results of Stiffler on the decomposition of ℛ-trivial monoids and locally ℛ-trivial semigroups. A small modification of the argument provides a new proof of a recent theorem of Bojańczyk, Straubing and Walukiewicz on the decomposition of forest algebras.
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