Local loop lemma

  title={Local loop lemma},
  author={Miroslav Olvs'ak},
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. 
Twitter Mention


Publications referenced by this paper.