evaluation homomorphism for free algebras

Let \(R,R'\) be rings, \(\varphi: R \rightarrow R'\) a ring-homomorphism Let \(X_i\) be a set and \(\mathrm{free}[X_i]\) the free algebra and \(A\) an \(R'\)nAlgebra.

Then for the free algebra

Algebra-Einsetzungshomomorphismus

adjoint-ness