Given a binary relation from to , its opposite relation (or dual, inverse, converse, reverse, etc) is a relation from to as follows:
- is -related to if and only if is -related to .
Note that .
The operation is part of the requirements for Rel to be an allegory.
If is a function thought as a functional entire relation, then is also a function if and only if is a bijection; in that case, is the inverse of .
More generally, we have the following:
|If is …||then is …|
If is a partial order (or even a preorder), then so is ; so each poset (or proset) has an opposite poset (or proset), which is a special case of an opposite category.
Revised on September 13, 2013 19:46:30
by Toby Bartels