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## Comments

A Lawvere metric space is a set of objects between which we have some sort of notion of a distance. It can be infinite which intuitively means that no matter the effort, sometimes you can't get from a point \( a \) to the point \( b \). On the other hand, a category \( \mathcal{X} \) enriched in \( (\mathbb{R_{\geq_0}}, \geq, 0, +) \) defines a finite distance between every two of its objects. This means that we

canget from point \( a \) to point \( b \), for any two points \( a, b \in \mathcal{X} \).`A Lawvere metric space is a set of objects between which we have some sort of notion of a distance. It can be infinite which intuitively means that no matter the effort, sometimes you can't get from a point \\( a \\) to the point \\( b \\). On the other hand, a category \\( \mathcal{X} \\) enriched in \\( (\mathbb{R_{\geq_0}}, \geq, 0, +) \\) defines a finite distance between every two of its objects. This means that we _can_ get from point \\( a \\) to point \\( b \\), for any two points \\( a, b \in \mathcal{X} \\).`