The posetal reflection of a preorder is the poset obtained by enforcing antisymmetry by quotienting out isomorphisms.
Let be a preorder. Define the equivalence relation:
The corresponding posetal reflection of is the preorder on the quotient given by
It’s easy to show both and are well-defined.
Abstractly, the correspondence is functorial from preorders to posets, and in fact exhibits Pos as a reflective subcategory of preorders (hence the name).
Last revised on November 26, 2024 at 11:46:46. See the history of this page for a list of all contributions to it.