Iterated chromatic localisation

Understand

We study a certain monoid of endofunctors of the stable homotopy category that includes localizations with respect to finite unions of Morava $K$-theories.

• We work in an axiomatic framework that can also be applied to analogous questions in equivariant stable homotopy theory.
• Our results should be helpful for the study of transchromatic phenomena, including the Chromatic Splitting Conjecture.
• The combinatorial parts of this work have been formalised in the Lean proof assistant.