Example 2

Take $\mathscr{T}$ to be the theory of sets, and consider the species of structures which has no auxiliary base set, one principal base set $\mathrm{A}$, the typical characterization $\mathrm{F} \in \mathfrak{P}((\mathrm{A} \times \mathrm{A}) \times \mathrm{A})$, and as axiom the transportable relation "F is a functional graph whose domain is $\mathrm{A} \times \mathrm{A}$". The structures of this species are particular cases of what are called algebraic structures, and the function whose graph is $\mathrm{F}$ (a mapping of $\mathrm{A} \times \mathrm{A}$ into $\mathrm{A}$) is called the (everywhere defined) internal law of composition of such a structure.