Generic model of an algebraic theory
= Generic model of an algebraic theory
{title2=$U_S(A)=A_S$}
In $[\mathbb T_{fp},\mathbf{Set}]$, the generic model assigns to each finitely presented algebra its underlying set at each sort, with the algebraic operations pointwise. It is covariant on algebra homomorphisms. Pullback along a geometric morphism yields its classified internal model.