Early in our mathematical education, we learn about a strong
interplay between algebra and geometry—algebraic equations give rise
to graphs and geometric figures, and geometric features can be
encoded in algebraic expressions. It’s almost as if there’s a portal
or bridge connecting these two realms in the grand landscape of
mathematics: whatever occurs on one side of the bridge is mirrored
on the other.

So although algebra and geometry are very different areas of
mathematics, this connection suggests that they are intrinsically
related. Incidentally, the `bridge’ that spans them is a but a dim
foreshadow of much deeper connections that exist between other
branches of mathematics that also may, a priori, seem unrelated: set
theory, group theory, linear algebra, topology, graph theory,
differential geometry, and more. And what’s amazing is that these
relationships—these bridges—are more than just a neat
observation. They are *mathematics*, and that mathematics has a name:
*category theory*.