partial order of natural numbers

notation: $(\mathbb{N},\leq)$
objects: natural numbers $0, 1, 2, \dotsc$
morphisms: a unique morphism $(n,m) : n \to m$ if $n \leq m$
Related categories: $(\mathbb{N}_\infty, \leq)$ , $(\mathbf{On},\leq)$ , $(\mathbb{Z},\mid)$

This can also be seen as the path category of the infinite linear graph $\bullet \to \bullet \to \bullet \to \cdots$ .

Properties from the database

Deduced properties

Non-Properties from the database

Deduced Non-Properties*

*This also uses the deduced properties.

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