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Topic: Homomorphism of posets and lattices
Replies: 16   Last Post: Sep 20, 2013 6:22 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Homomorphism of posets and lattices
Posted: Sep 18, 2013 12:20 AM
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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.

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