The category of posets we denote by $Poset$. $Poset$ has arbitrary limits, colimits, exponentials, and a restricted subobject classifier. ## Reference * Lauri Tart, subobject classification and geometric morphisms of partially ordered acts, masters thesis, [pdf](http://dspace.utlib.ee/dspace/bitstream/handle/10062/593/tart.pdf;jsessionid=5EBFF22A72777356EC8E9693CF254B74?sequence=5)