To give an answer on a fairly concrete level―I don't know a lot of category theory, but one interesting insight I've gained from my limited study of it, which has convinced me that it's worth learning, is about the notion of products of structures.
Most mathematics probably acquire an informal understanding of the notion of the products of structures before they study category theory. In the simplest cases we can say that taking the product of some structures is just the act of going from looking at individual elements to looking at composite elements that are made up of parts, and applying operations to these composites by distributing those operations over those parts.... (read 731 more words →)
To give an answer on a fairly concrete level―I don't know a lot of category theory, but one interesting insight I've gained from my limited study of it, which has convinced me that it's worth learning, is about the notion of products of structures.
Most mathematics probably acquire an informal understanding of the notion of the products of structures before they study category theory. In the simplest cases we can say that taking the product of some structures is just the act of going from looking at individual elements to looking at composite elements that are made up of parts, and applying operations to these composites by distributing those operations over those parts.... (read 731 more words →)