ag.algebraic geometry - Lie bracket on the unshifted tangent complex?

touchstone principle – Is intersection of two product $sigma$-algebras is too a product $sigma$-algebra? Answer

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touchstone principle – Is intersection of two product $sigma$-algebras is too a product $sigma$-algebra?

Given a quadruple of measurable areas $(A,mathcal{A})$,
$(A,mathcal{A}’)$, $(B,mathcal{B})$, $(B,mathcal{B}’)$ is it
undoubted that
$mathcal{A}otimesmathcal{B}capmathcal{A}’otimesmathcal{B}’$
is too a product of some $sigma$-algebras on $A$ and $B$? I
would speculate the respond is “no”, however how would one inform that an
$sigma$-algebra $mathcal{C}$ on $Atimes B$ is just not a product, aside from the
trifling “too few cylinder-sets”?

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