  We present a six-dimensional $\mathcal{N}=(1,0)$ supersymmetric higher gauge
theory in which self-duality is consistently implemented by physically trivial
Lagrange multipliers. The action contains both $\mathcal{N}=(1,0)$ tensor and
vector multiplets and is non-trivially interacting. The tensor multiplet part
is loosely related to a recently proposed action by Sen that leads to on-shell
self-duality in an elegant way. As we also show, Sen's action finds a very
natural and direct interpretation from a homotopy algebraic perspective.
