Relatively parametrizable subalgebras (Q1840716)

In a previous paper [``Parametrizable algebras'', J. Lond. Math. Soc., II. Ser. 8, 750-752 (1974; Zbl 0296.08018)], the author proved that a universal algebra \(A\) is parametrizable iff it is projective in the variety which \(A\) generates. Here, he does the same for \(k\)-parametrizability and \(k\)-projectivity. He calls an algebra \(A\) \(k\)-projective if for each surjective homomorphism \(f:X\to Y\), each homomorphism \(g:A\to Y\) and each \(k\)-generated subalgebra \(i:B\to A\), there exists a homomorphism \(h:B\to X\) with \(fh=gi\).