# Local loop lemma

@inproceedings{Olvsak2019LocalLL, title={Local loop lemma}, author={Miroslav Olvs'ak}, year={2019} }

- Published 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.