  In order to get $\lambda$-models with a rich structure of $\infty$-groupoid,
which we call "homotopy $\lambda$-models", a general technique is described for
solving domain equations on any cartesian closed $\infty$-category (c.c.i.)
with enough points. Finally, the technique is applied in a particular c.c.i.,
where some examples of homotopy $\lambda$-models are given.
