Changes

: <math>f(x_1, \ldots, x_n) ~=~ (fx_1, \ldots, fx_n).\!</math>

: <math>f(x_1, \ldots, x_n) ~=~ (fx_1, \ldots, fx_n).\!</math>

A '''relation homomorphism''' from a <math>k\!</math>-place relation <math>P \subseteq X^k\!</math> to a <math>k\!</math>-place relation <math>Q \subseteq Y^n\!</math> is a mapping between the underlying sets, <math>h : X \to Y,\!</math> whose induced action <math>h : X^n \to Y^n\!</math> preserves the indicated relations, taking every element of <math>P\!</math> to an element of <math>Q.\!</math> In other words:

A "relation homomorphism" from an n place relation P c Xn to an n place relation Q c Yn is a mapping between the underlying sets, h : X >Y, whose induced action h : Xn >Yn preserves the indicated relations, taking every element of P to an element of Q.  In other words:

<x1, ..., xn> C P   =>  h(<x1, ..., xn>) C Q.

: <math>(x_1, \ldots, x_k) \in P \mapsto h(x_1, \ldots, x_k) \in Q.\!</math>

Applying this definition to the case of two binary operations or LOCs, say *1 on X1 and *2 on X2, which are special kinds of triadic relations, say *1 c X13 and *2 c X23, one obtains:

Applying this definition to the case of two binary operations or LOCs, say *1 on X1 and *2 on X2, which are special kinds of triadic relations, say *1 c X13 and *2 c X23, one obtains: