Jaime Sevilla Molina I've submitted an edit to the page on morphisms and wrote an intuitive guide to isomorphisms. I hope it's suitable for now.
My plan is also eventually to write an intuitive guide to categories with lots of concrete examples which hopefully tie in to some real-world ideas and are not as reliant on abstract mathematics.
However, I'd like to get some of the basic concepts down for the sake of the main lens. Also I'm formally trained in pure math so these are the setting and examples with which I'm more familar.