[winwang]

https://en.wikipedia.org/wiki/Commutative_diagram

[Garlef]

I think Double Categories [1] would be a more appropriate setting: In a double category, the vertical and horizontal arrows are of different types. In usual commutative diagrams, they are of the same type.

[1]: https://ncatlab.org/nlab/show/double+category

[noqc]

Commutative diagrams are to these squares what category theory is to analogy.

[ogogmad]

There's a mapping there, however it's not natural.

[gowld]

noqc, can you diagram your comment?

[ogogmad]

Why don't some phrases arrive at the same meaning? They don't commute.