A Lawvere metric space
A Cost-category, i.e. a category enriched in the symmetric monoidal preorder \(\mathbf{Cost}=([0,\infty],\geq,0,+)\).
\(X\) is given as \(Ob(\mathcal{X})\)
\(d(x,y)\) is given as \(\mathcal{X}(x,y)\)
The axiomatic properties of a category enriched in Cost are:
\(0 \geq d(x,x)\)
\(d(x,y)+d(y,z) \geq d(x,z)\)