lattice homomorphism
nounUK /ˈlætɪs ˌhɒməˈmɔːfɪzəm/
US /ˈlætɪs ˌhoʊməˈmɔːrfɪzəm/
A rule that keeps the meet and join of a lattice the same when you map it to another lattice.
The map sending each set to its complement is a lattice homomorphism on the power set lattice.
RELATED WORDS
OTHER MEANINGS
2. A function between lattices that preserves both binary operations, meet and join.
Every lattice homomorphism preserves finite meets and joins.
3. A map f with f(a∧b)=f(a)∧f(b) and f(a∨b)=f(a)∨f(b) for all elements a and b.
Checking the two equations confirms that f is a lattice homomorphism.
4. A structure-preserving map in the category of lattices.
Lattice homomorphisms are the morphisms in the category of lattices.