English

Local loop lemma

Logic 2019-02-26 v1 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1902.08791,
  title  = {Local loop lemma},
  author = {Miroslav Olšák},
  journal= {arXiv preprint arXiv:1902.08791},
  year   = {2019}
}
R2 v1 2026-06-23T07:48:52.480Z