A beautiful intuition on associativity

I found a beautiful explanation about what property does the associativity capture: You can think of each element of a monoid as having two sides. The idea is that the left side and right side are independent things that don’t interfere with each other. For example, adding some stuff at the beginning of a list, and adding some stuff at the end of a list, don’t affect each other, and it doesn’t matter which you do first. That’s the idea that associativity captures.

from here

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