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Can anyone clarify what precisely is meant by "nonlocal transformations" in the BV formalism?

Specifically, they claim that for any gauge theory with an open algebra, it is possible to go to a different basis for the algebra whereby one achieves closure (and even one where the gauge algebra is always abelian!). They claim this is at the price that the infinitesimal transformations (the usual stuff, where the transformation of the field is proportional to the algebra generators) be nonlocal and non relativistic covariant.

I guess I'm trying to understand how related this is to my beloved local and covariant gauge theories, say non-Abelian Yang-Mills. Can anyone elaborate on the statements that "if I drop locality and covariance for Yang-Mills theory, then the theory becomes abelian?" or "if I drop locality and covariance for supergravity, then the algebra can always be closed?"

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# A Nonlocal transformations in Batalin-Vilkovisky theory

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