A category whose isomorphisms induce an equivalence relation coarser than shape

Let Sh denote the usual shape category of metric compacta. In the paper one defines a new category S ∗ , whose objects are all metric compacta, and one defines a functor S ∗ : Sh → S ∗ , which preserves objects. In shape fibrations over a metric continuum fibers need not have the same shape, but they are isomorphic objects of S ∗ . Various shape invariant classes of compacta, like FANRʹs and movable continua, are also S ∗ -invariant classes, i.e., if X and X ′ are isomorphic objects in S ∗ and X is an FANR (is movable), then so is X ′ . Compact ANRʹs are isomorphic in S ∗ if an only if they have the same homotopy type.