Locality compatibility of the universal enveloping ideal

Let $(\mathfrak{g},\top_{\mathfrak{g}},[\,\ ])$ be a locality Lie algebra, let $\mathcal{T}_\top(\mathfrak{g})$ be its locality tensor algebra, and let $J_\top(\mathfrak{g})$ be the ideal introduced in the definition of the locality universal enveloping algebra. Universal enveloping ideal conjecture. The ideal

$$J_\top(\mathfrak{g})$$

is locality compatible with $\top_\otimes$. This compatibility is the condition needed for the quotient defining the locality universal enveloping algebra to inherit a locality structure; the paper adopts it as a further assumption in its study of the locality Milnor–Moore framework.