Add solution to I.5.5

[BillXWB]

Added a missing solution.

[hooyuser]

Nice work! Generally looks good to me. A possible improvement can be emphasizing such $\sigma$ will make the diagram commute, which justifies $\sigma$ as morphisms in that considered category.

If we are to find all final objects, some more care should be taken. Besides the functions with a singleton range, all the functions with a singleton image should also satisfy the universal property. And one can show that there exist no other final objects. If there exists such an $f$, considering an arrow in that considered category from $\sigma$ to $f$ will lead to a contradiction.