Nice Introduction to Category Theory
Posted by Ed on July 21, 2009
A picture is worth a thousand words. I can confirm this for the nice introduction to category theory by jao. I’ve tried to understand category theory some time ago but all I remember is that a category consists of a class of objects and a class of arrows. Then I discover this little jem with a text accompanied by beautiful diagrams and suddenly it becomes all very intuitive and clear, even the functors. Somehow, functors remind of the isomorphism between two graphs. By the way, you can consider Haskell as a category with the types as objects and the functions as arrows.
A somewhat related blogpost is the one by Benjamin L. Russell about category theory in Haskell. He also writes about his personal “math story” describing how he overcame his math phobia and found his love for abstract mathematics.
In Learning Haskell through Category Theory, and Adventuring in Category Land: Like Flatterland, Only About Categories Russell also includes literature on category theory.
In Abstraction, intuition, and the “monad tutorial fallacy” Brent Yorgey writes about the importance of understanding a concept in your own way and that your “Aha moment” might not cause an “Aha moment” for others.
Benjamin L. Russell said
>A somewhat related blogpost is the one by Benjamin L. Russell about category
>theory in Haskell. He also writes about his personal “math story” describing
>how he overcame his math phobia and found his love for abstract mathematics.
Thank you for your reference.
Actually, I would qualify “abstract mathematics” as “theoretical mathematics related to set theory, recursive function theory, and mathematical logic.”
I wrote about category theory because it is related to Haskell; however, since category theory focuses on morphisms between mathematical structures, rather than what lies within the structures, the style of thinking is quite different from that of set theory, and takes quite a lot of familiarization. More precisely, “love for abstract mathematics” could be restated as “interest in theoretical mathematics related to set theory, recursive function theory, and mathematical logic, and desire to learn branches of mathematics related to Haskell.” Were category theory not related to Haskell, I would probably not study it, since it more of a flavor of algebra than set theory or logic.
Ed said
Thanks for your comment.
I also wouldn’t study category theory for the sake of it. But for a friend of mine it is the converse. He likes category theory and he just wants to learn Haskell because you can “do” some category theory with it.