  We consider conditional transition systems, that model software product lines
with upgrades, in a coalgebraic setting. By using Birkhoff's duality for
distributive lattices, we derive two equivalent Kleisli categories in which
these coalgebras live: Kleisli categories based on the reader and on the
so-called lattice monad over $\mathsf{Poset}$. We study two different functors
describing the branching type of the coalgebra and investigate the resulting
behavioural equivalence. Furthermore we show how an existing algorithm for
coalgebra minimisation can be instantiated to derive behavioural equivalences
in this setting.
