[d_tr]

It would help if you read the definition of a category. It is very abstract but also pretty simple with just a couple of axioms.

An example of a category is the "sets and functions" category. In that category, every conceivable set lives as an object (node) and every conceivable function between any two sets lives as an arrow between these two sets.

So, you can take an arrow from A to B and one from B to C and compose them like you would do with functions to get a function from A to C.

A commutative diagram would then be a subset of the whole category, where following all depicted paths between two sets X and Y would yield the same function if for each path you composed all the arrows belonging to it.

I haven't read anything on higher categories so I am not sure about pasting diagrams, but they are probably something along these lines, generalized in some way.

[d_tr]

It would help if someone could tell what's wrong in my reply.

[keithalewis]

You made a completely obvious and true statement starting with "It would help..." That seems to be frowned upon on HN.

BTW, a simpler definition of a (small) category is that it is a partial monoid.

[xanderlewis]

You mean a monoidoid.

(I’m not sure this ‘simpler definition’ is going to help!)

[CJefferson]

I didn't downvote you, but honestly, it doesn't really help understand what commuting diagrams are. I use them all the time, and never use category theory.

Your description was all abstraction, and I can't imagine would help anyone who didn't already know what we are talking about.

A concrete example would greatly help!