I’m sure we’ve all heard of the Yoneda Lemma before, but why does it get so much hype in category theory when the result itself is quite elementary to prove? Well, you’re not going to get a good answer from me.

When you hear that someone is “studying algebra”. What comes to mind? Are they drilling through thousands of factorisation problems? Are they an undergraduate student of mathematics, pursuing studies you can’t think of any real-world applications for? Well, you’re all wrong (or maybe you’re not).

A colimit is just a limit in the opposite category, what’s the problem?

Despite being formally dual to monads, they don’t seem to be “all the rave” like monads are. Just because you get ‘em by just reversing some arrows doesn’t mean that comonads aren’t independently interesting!

The “opposite” of being finite is having a finite complement. The “opposite” of a vector is a linear functional. If a set is a small collection of elements… then what is the “opposite” of a set?