Mathematicians, I have a confession...

I've never actually performed a diagram chase.

But I've followed several chases, and I think... isn't there a better way? Sometimes I marvel that chases work at all, but it seems to me that they do because the definitions are all just set up in the right way. The real work was in the definitions, not in the chases.

So aren't there "deeper", more insightful proofs than the canonical diagram chases?

@acciobooks It's a technique proof in homological #algebra and sometimes in general #CategoryTheory. You draw a diagram of objects and morphisms and you want to determine something about it, that something is a homomorphism or that some part of the diagram commutes. So you look at each point, you pick an arbitrary element, and you use known properties of the diagram to reach the desired conclusion as you "chase" elements around the diagram.

This is an example in a movie:

https://www.youtube.com/watch?v=etbcKWEKnvg

@JordiGH Huh, that's interesting. I'm not quite sure that I understand, but it sure looks cool.

@JordiGH A diagram is just a good way of organizing information. I would argue that the diagram chase is indeed the most insightful proof. I would suggest actually doing some proofs by diagram chase before you question their usefulness!

Accio Books!@acciobooks@mastodonten.de@JordiGH What is a diagram chase?