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## Comments

The preorder reflection of a category identifies all morphisms with the same source and target. It follows that any monoid (i.e., category with one object), is taken to the trivial preorder (the preorder with one element) under preorder reflection. So, in particular, \(\mathbb{N}\) has the trivial preorder as its preorder reflection.

`The preorder reflection of a category identifies all morphisms with the same source and target. It follows that any monoid (i.e., category with one object), is taken to the trivial preorder (the preorder with one element) under preorder reflection. So, in particular, \\(\mathbb{N}\\) has the trivial preorder as its preorder reflection.`