I am quite new to categories and the book I am reading is Lawvere and Schanuel's Conceptual Mathematics.
At the end of Part 2 the authors use the proof of Brouwer's fixed point theorems as an example of how one can use category thinking to construct proofs, by 'objectification' and 'mapification'.
I guess this process is very important if one really want to use category to deepen understanding. However, I found this part rather difficult. I wonder whether there are some other examples that show the power of categorifying proofs.
All examples are welcome. Thanks!