Example 4

\* When each of $\Sigma$ and $\Theta$ is the species of group structures (resp. ring structures), there is defined in algebra a procedure of deduction which associates with each group structure (resp. ring structure) the group structure (resp. ring structure) on its centre. When $\Sigma$ is the species of vector space structures over a field $K$, and when $\Theta$ is the species of algebraic structures over $K$, there are defined procedures of deduction which associate with every vector space over $K$ its tensor algebra or its exterior algebra. We shall meet many other examples later in this series. \*