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# Exercise 21 - Chapter 3

edited June 2018

What is the preorder reflection of the category $$\mathbb{N}$$.

$$Path = \{z, s, s.s, s.s.s, \cdots \}$$ $$\mathbb{N} = \{0, 1, 2, 3, \cdots \}$$ Previous Next

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.
Comment Source: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.