In an article by A. Borovik, “Is mathematics special?”, he talks about the fact that [carrying is a cocycle][1]. He then says > [A student] discovered that carry is doing what cocycles frequently do: they are responsible for break of symmetry. I have never thought about cocycles in this way. In what sense are cocycles often breaking symmetry? Are there any other examples of this? [1]: https://ncatlab.org/nlab/show/carrying