Absolute cartesian–cocartesian equivalence conjecture for cubes of spaces

Let an $n$-cube be a diagram of spaces indexed by the powerset of $[n]=\{0,1,\ldots,n\}$. A diagram is absolutely cartesian if every homotopy functor sends it to a homotopy cartesian diagram, and absolutely cocartesian if every homotopy functor sends it to a homotopy cocartesian diagram. Absolute cartesian–cocartesian equivalence conjecture. An $n$-cube is absolutely cartesian if and only if it is absolutely cocartesian. The paper observes that absolutely cartesian squares are also absolutely cocartesian, but states that the equivalence for general $n$-cubes is an additional conjecture whose status is not settled.