A thin or posetal category a category in which, given any two objects and and any two morphisms and from to , the morphisms and are equal:
Up to isomorphism, a thin category is the same thing as a proset (a preordered set). Up to equivalence, a thin category is the same thing as a poset. So mostly we just talk about posets here, but some references want to distinguish these from thin categories. (It is really a question of whether you're working with strict categories, which are classified up to isomorphism, or categories as such, which are classified up to equivalence.)
A poset is a thin category. In particular so are (semi)lattices, Heyting algebras and frames.
specializaton order?
Last revised on May 3, 2022 at 15:41:28. See the history of this page for a list of all contributions to it.