quality:correction, information:classification
Cauchy completion of categories

Krause (2020) introduced a notion of Cauchy completion of a category. Applied to Q {\displaystyle \mathbb {Q} } (the category whose objects are rational numbers, and there is a morphism from x to y if and only if x ≤ y {\displaystyle x\leq y}), this Cauchy completion yields R ∪ { ∞ } {\displaystyle \mathbb {R} \cup \left\{\infty \right\}} (again interpreted as a category using its natural ordering).