Homomorphisms of direct powers of algebras (Q5896812)

A universal algebra \(A\) is called \(n\)-coconnected, for a given positive integer \(n\), if every homomorphism \(A^n\to A\) factorizes through a product projection (i.e., it depends on at most one coordinate). Fully coconnected algebras are those \(n\)-coconnected for every positive integer \(n\). The author solves the problem of whether every 3-coconnected algebra is fully coconnected: Main theorem: The variety of all algebras with two unary operations contains, for every positive integer \(n\geq 2\), a finite \(n\)-coconnected algebra that is not \((n+1)\)-coconnected.