“Diagram chasing”, which is the standard method of reasoning in Category Theory, turns out to be very useful in other branches of mathematics, such as topology.

“Diagram chasing”, which is the standard method of reasoning in Category Theory, turns out to be very useful in other branches of mathematics, such as topology. (By the way, do not underestimate the power of abstract algebra, it’s widely used in the rest of mathematics, and its applicability to computing is more obvious.)