Here's a **Puzzle** using Chapter 3's concepts:

Consider your favorite database schema \$$\mathcal{C}\$$. Suppose you have two instances of the databases that you wish to merge. Let \$$I:\mathcal{C}\to\mathbf{Set}\$$ and \$$J:\mathcal{C}\to\mathbf{Set}\$$ be the instances of each database. For example, company A (database \$$I\$$) and company B (database \$$J\$$) are merging their employee records, and luckily for you, both databases have the same structure \$$\mathcal{C}\$$.

Merging these databases is equivalent to a universal construction in a certain category. What is the construction and in what category? Here's a hint, the merged database is another instance of \$$\mathcal{C}\$$ so call it \$$K:\mathcal{C} \to \mathbf{Set} \$$.