Let $\mathbf{Poset}$ be the category of partially ordered sets with order-preserving maps. Does $\mathbf{Poset}$ have both pushouts and pullbacks?



Does the category of posets have pushouts and pullbacks?
Yes it is complete and cocomplete because it is locally presentable. Of course, a colimit of posets will "crush" all loops because of antisymmetry. In particular, it has pushouts and pullbacks.


