On Wikipedia, Tarski schema T says:
A sentence of the form "A and B" is true if and only if A is true and B is true
A sentence of the form "A or B" is true if and only if A is true or B is true
A sentence of the form "not A" is true if and only if A is false
Can Tarsi's schema T be viewed as a homomorphism? The case of a negation seems problematic?
Let $L$ be a first-order language. Schema T can be viewed as a homomorphism from the Boolean algebra of sentences of $L$ (modulo logical equivalence) to the two-element Boolean algebra. More generally, let $W$ be a theory over $L$, and consider the Boolean algebra $A$ of sentences of $L$, modulo $W$-equivalence. Then the schema can be thought of as a homomorphism from $A$ to the two-element Boolean algebra. For more information, please see the Wikipedia article on the Lindenbaum Algebra.