On day 16 we looked at some concrete categories using Awodey’s ‘Category Theory’ as the guide.
We can now talk about abstract structures today. 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 definition of isomorphism is one such example:
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.
We can use this notion of isomorphism as a building block to explore more concepts.