Posets as categories
A poset may be viewed as a Posetal category (with
- reflexivity and transitivity are equivalent to identity and composition in the definition of a category, but since we have at most one way of relating
to this is a Thin category. - antisymmetry is equivalent to the condition of being Skeletal category.
In addition
- A monotone mapping is a functor of posets-as-categories
- A totally ordered set is a connex category
- The supremum is the coproduct
- The infimum is the categorical product
#state/tidy | #lang/en | #SemBr