[[Things as categories]] # Posets as categories A [[poset]] may be viewed as a [[Posetal category]] (with $a \to b$ denoting $a \leq b$) and vice versa, where - 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 $a$ to $b$ 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 [[Poset#^sup]] is the [[Products and coproducts|coproduct]] - The [[Poset#^inf]] is the [[Products and coproducts|categorical product]] # --- #state/tidy | #lang/en | #SemBr