Local loop lemma

@inproceedings{Olvsak2019LocalLL,
  title={Local loop lemma},
  author={Miroslav Olvs'ak},
  year={2019}
}
We prove that an idempotent operation generates a loop from a strongly connected digraph containing directed cycles of all lengths under very mild (local) algebraic assumptions. Using the result, we reprove the existence of a weakest non-trivial idempotent equations, and that a strongly connected digraph with algebraic length 1 compatible with a Taylor term has a loop. 
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