Hey Chris,

I think you mean:

> If we have a pair \$$f \dashv g: \mathcal{X} \to \mathcal{Y}\$$ of adjoint short-maps then can we construct an equivalence between \$$\mathcal{X}\$$ and \$$\mathcal{Y}\$$?

Contraction mappings are Lipschitz continuous functions with constants \$$k < 1\$$, while short-maps correspond to \$$\mathbf{Cost}\$$-functors.

I don't know the answer to this.