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In this paper we further investigate the geometry of monads oforder-preserving functionals and of positively homogeneous functionals. Weprove that for any compactum X with $w(X) = \tau$ the map $\mu_F X$, where$F\in\{O,OH\}$, is homeomorphic to trivial $I^\tau$-fibration if and only if$X$ is openly generated $\chi$-homogeneous compactum.

Trivial fibrations of the multiplication maps for monads generated by the functors of order-preserving and positively homogeneous functionals