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.

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.