### Category Theory Puzzle

#### Posted by John Baez

One nice thing about category theory is that despite its soaringly ambitious nature, it still contains hundreds of satisfying little puzzles to entertain the problem-solver in us. James Dolan likes to give me these puzzles and see how long it takes me to solve them. While I find it a bit distressing to be put on the spot like that, they’re still fun.

Here’s the one he gave me yesterday. See how long it takes you.

Suppose $C$ is an $Ab$-enriched category: that is, its homsets are abelian groups and composition is bilinear. Suppose $x \in C$ is a terminal object. Show that $x$ is initial.

## Re: Category Theory Puzzle

Good puzzle! Do I detect Jim’s hand in calling an object of a category “$x$”?

Maybe you should tell us who’s allowed to post an answer.