Conjecture. If the $V$ cone generated by the points in the matrix $A$ has an $H$ representation captured by matrix $B$, and $A = A_1 \otimes A_2$, $B = B_1 \otimes B_2$, where $B_1$ is the $H$ representation of the cone generated by the points in $A_1$, and $B_2$ is the $H$ representation of the cone generated by the points in $A_2$, $\otimes$ is the Kronecker product; then the $B$ cone generated by the points in $A_1 \otimes A_2$, has an $H$ representation with matrix $B_1 \otimes B_2$.
Do you know if someone has established this conjecture to be true?
Please do take into account this is a generalization of the Weyl-Minkowski theorem. I am asking for a paper or book where you think I could find it. Apologies if this kind of question is not allowed. I have done the $2 \times 2$ case and it works. But not sure about the general problem.