Abstract
AbstractIf F is a (not necessarily associative) monad on Set, then the natural transformation $$F(A\times B)\rightarrow F(A)\times F(B)$$F(A×B)→F(A)×F(B) is surjective if and only if $$F(\varvec{1})=\varvec{1}$$F(1)=1. Specializing F to $$F_{\mathcal {V}}$$FV, the free algebra functor for a variety $$\mathcal {V},$$V, this result generalizes and clarifies an observation by Dent, Kearnes and Szendrei in 2012.
Funder
Philipps-Universität Marburg
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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