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In an article by A. Borovik, “Is mathematics special?”, he talks about the fact that carrying is a cocycle. 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?

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  • $\begingroup$ Why was this question deemed more appropriate for MO than Math SE? This is not by any means a strictly research-level question, but rather one about some intuition, and the topic is not highly specialized (we've had questions on group cohomology here). I'm just curious what reasoning stood behind that decision. $\endgroup$ – Wojowu Dec 22 '18 at 13:37
  • $\begingroup$ @Wojowu I asked this on Stackexchange, but did not get an answer and was hoping to get one here. $\endgroup$ – berndibus Dec 22 '18 at 19:03

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