Exercise 1, § 3

Let E be a topological space and let $\Sigma$ be one of the species of structures defined in Exercises 7 and 8 of § 2. Take the morphisms to be those defined in the same exercises, and the $\alpha$-mappings to be the continuous mappings of E into a $\Sigma$-set. Show that the universal mapping problem for E (relative to the preceding definitions) has in general no solution. \*