Exercise 2, § 3

Let E be a field, $\Sigma$ the species of algebraically closed field structures. Take the morphisms to be homomorphisms, and the $\alpha$-mappings to be homomorphisms of E into an algebraically closed field. Show that the algebraic closure $\mathrm{F_E}$ of E and the canonical injection of E into $\mathrm{F_E}$ satisfy $(\mathrm{AU'_I})$, but that there is in general no solution to the universal mapping problem for E. \*