Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
A linear order could refer to either
a strict total order (i.e. DLO)
Classically, the first two are the same, but constructively, the second notion is weaker than the first.
Classically, the first and third are complements of each other - and thus defining one is sufficient to defining the other, they still have different properties. In constructive mathematics, only the decidable such relations are complements of each other, and in general the two relations cannot be defined from the other.
Last revised on December 26, 2023 at 04:49:14. See the history of this page for a list of all contributions to it.