A thin category or posetal category is a category in which, given a pair of objects and and any two morphisms , the morphisms and are equal:
Another synonym is (0,1)-category.
Up to isomorphism, a thin category is a preordered set (“proset”). Up to equivalence, a thin category is the same thing as a partially ordered set (“poset”).
For more on this see at relation between preorders and (0,1)-categories.
A poset is a thin category. In particular so are (semi)lattices, Heyting algebras and frames.
Last revised on September 22, 2022 at 18:42:24. See the history of this page for a list of all contributions to it.