Thin category or posetal category is a category where for every hom-set, it is either empty or a singleton set (one element). i.e., there is at most one arrow between any two objects per direction.
Thin category is isomorphic to preorder (see Order).
Preorder is a binary relation (≤) that is reflexive and transitive.
- reflexivity gives the identity
- transitivity gives the composition
Why is it called posetal category if it’s isomorphic to preorder (not poset)?
- the requirement for hom-set to be empty or contain one element does not give antisymmetry as