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The category $\mathbb{R}$ is defined as a poset category where the objects are real numbers, and there is a morphism $x \to y$ exactly when $x \le y$. This means the morphisms encode the ordinary order relation on the real numbers.

Conditions: Objects are real numbers.; A morphism $x\to y$ exists precisely when $x\le y$.

The category $\mathbb{R}$ is defined as a poset category where the objects are real numbers, and there is a morphism $x \to y$ exactly when $x \le y$. This means the morphisms encode the ordinary order relation on the real numbers.

Conditions: Objects are real numbers.; A morphism $x\to y$ exists precisely when $x\le y$.