On day 15 we started looking at basic concepts in category theory using Lawvere and Schanuel’s Conceptual Mathematics. The book is a good introduction book into the notion of category because it spends a lot of pages explaining the basic concepts using concrete examples. The very aspect gets a bit tedious when you want to move on to more advanced concept, since it’s goes winding around.
Today I’m switching to Steve Awodey’s Category Theory. This is also a book written for non-mathematicians, but goes at faster pace, and more emphasis is placed on thinking in abstract terms.
A definition or a theorem is called abstract, when it relies only on category theoric notions, rather than some additional information about the objects and arrows. The advantage of an abstract notion is that it applies in any category immediately.
Definition 1.3 In any category C, an arrow f: A => B is called an isomorphism, if there is an arrow g: B => A in C such that:
g ∘ f = 1A and f ∘ g = 1B.
Awodey names the above definition to be an abstract notion as it does make use only of category theoric notion.
Another good book to read together is Bartosz Milewski (@bartoszmilewski)’s Category Theory for Programmers that he’s been writing online.