
Homomorphism of posets and lattices
Posted:
Sep 18, 2013 12:20 AM


What's your opinion about the following except from a manuscript?
I consider the Definition 2.92 to be in error unless the domain of the function is a linear order. For example, the identity function from a two point antichain { a,b } to the chain a < b.
Comments? Are not antichains preserved by order isomorphisms?
2,1,12 Homomorphism of posets and lattices
Definition 2.90. A monotone function (also called order homomorphism) from a poset A to a poset B is such a function f that x <= y > f(x) <= f(y).
Definition 2.91. Order embedding is an injective monotone function.
Definition 2.92. Order isomorphism is an surjective order embadding (= bijective monotone function).
Order isomorphism preserves properties of posets, such as order, joins and meets, etc.
Definition 2.93.

