Product formula conjecture for Lusternik–Schnirelmann categories of compact Lie groups

Let $G$ be a simply-connected compact Lie group with

$$G=\prod_{i=1}^{n}H_i,$$

where each $H_i$ is a simple Lie group. Product formula conjecture. The weak category, ordinary category, and strong category of $G$ should coincide, and the ordinary category should be additive over the simple factors:

$$\operatorname{{\it w}cat}(G)=\operatorname{cat}(G)=\operatorname{Cat}(G),\qquad \operatorname{cat}(G)=\sum_{i=1}^{n}\operatorname{cat}(H_i).$$

The conjecture proposes a general product formula extending the computations and bounds established in the paper for low-rank simply-connected compact simple Lie groups and for $Sp(3)$.