  We generalise $\tau$-cluster morphism categories to non-positive proper dg
algebras. The compatibility of silting reduction with support $\tau$-tilting
reduction will be an essential ingredient when linking our definition to that
of Buan--Marsh. We also define two-term presilting sequences in the bounded
derived category in such a way that they correspond to signed
$\tau$-exceptional sequences in the module category.
