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} \\).