Poset (Category)

Note that this note discusses the category where every object is a poset. See Thin Category for the categorification of a single poset.

Definition

The category Poset is the category of partial orders and monotone maps.

Remarks

A $f$-prefixpoint is when $f(x)\le x$. A $f$-postfixpoint is when $f(x)\ge x$.

By Lambek’s lemma, a least prefixpoint is a fixed point.