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}
}