complete lattice homomorphism

Complete lattice homomorphism is a function from one lattice to an other lattice, which preserves arbitrary (not only finite) meets and joins.

If $\varphi :L\to M$ is lattice homomorphism between complete lattices $L$ and $M$ such that

• $\varphi (\bigvee \{a_i\mid i\in I\})=\bigvee \{\varphi (a_i)\mid i\in I\}$, and

• $\varphi (\bigwedge \{a_i\mid i\in I\})=\bigwedge \{\varphi (a_i)\mid i\in I\}$,

then $\varphi$ is called a complete lattice homomorphism.

Most often are considered complete lattice homomorphisms from one complete lattice to an other complete lattice (that is when all meets and joins are defined).

Complete lattice homomorphism is a special case of lattice homomorphism.

Title	complete lattice homomorphism
Canonical name	CompleteLatticeHomomorphism
Date of creation	2013-03-22 16:58:02
Last modified on	2013-03-22 16:58:02
Owner	porton (9363)
Last modified by	porton (9363)
Numerical id	6
Author	porton (9363)
Entry type	Definition
Classification	msc 06B23
Related topic	CompleteLattice