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.
Mark Chimes I am imagining myself in the shoes of somebody who doesn't know anything about cat theory getting frustrated when they find that the article keeps talking about morphisms without giving a clue of what they are.
I think that it would be valuable to spend some time working on an intuitive definition of morphism in its corresponding page to alleviate that.
I don't understand? A morphism is just an abstract element of a category. Its behaviour is completely characterized by the axioms of a category. It would be like formally defining an element of a set.
This is still very much a work in progress. Anyone is welcome to submit more info or edit. I'll add more details later. The current page probably won't remain the main lens.
I think this last edit is bad.
Please let me know why the edit is bad and I will improve it. I appreciate more constructive feedback.
It looks like there is a word missing from this sentence. I'm not sure what it is trying to say.
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.
Mark Chimes I am imagining myself in the shoes of somebody who doesn't know anything about cat theory getting frustrated when they find that the article keeps talking about morphisms without giving a clue of what they are.
I think that it would be valuable to spend some time working on an intuitive definition of morphism in its corresponding page to alleviate that.
I don't understand? A morphism is just an abstract element of a category. Its behaviour is completely characterized by the axioms of a category. It would be like formally defining an element of a set.
Probably you will want to precisely define morphism at some point, but I recommend you do it sooner rather than later to enforce coherence.
This is still very much a work in progress. Anyone is welcome to submit more info or edit. I'll add more details later. The current page probably won't remain the main lens.