  Given a family of groups admitting a braided monoidal structure (satisfying
mild assumptions) we construct a family of spaces on which the groups act and
whose connectivity yields, via a classical argument of Quillen, homological
stability for the family of groups. We show that stability also holds with both
polynomial and abelian twisted coefficients, with no further assumptions. This
new construction of a family of spaces from a family of groups recovers known
spaces in the classical examples of stable families of groups, such as the
symmetric groups, general linear groups and mapping class groups. By making
systematic the proofs of classical stability results, we show that they all
hold with the same type of coefficient systems, obtaining in particular without
any further work new stability theorems with twisted coefficients for the
symmetric groups, braid groups, automorphisms of free groups, unitary groups,
mapping class groups of non-orientable surfaces and mapping class groups of
3-manifolds. Our construction can also be applied to families of groups not
considered before in the context of homological stability.
  As a byproduct of our work, we construct the braided analogue of the category
FI of finite sets and injections relevant to the present context, and define
polynomiality for functors in the context of pre-braided monoidal categories.
