Reformulate the induction scheme (Definition 2.5.3) with respect to the reflexive relation.
X is then called an Lposet, and an Ldomain if it also has all directed joins. Formulate and prove an adjoint function theorem for Lposets. Show that if U:X® Y preserves wide pullbacks and is cofinal then it has a left adjoint. (Notice how introducing a degree of uniqueness improves the result by allowing us to drop the injectivity assumption.)


