## Complete distributive lattices

Abbreviation: CDLat

### Definition

A complete distributive lattice is a complete lattice $\mathbf{A}=\langle A,\bigvee,\bigwedge\rangle$ such that

$\vee$ distributes over $\wedge$: $x\vee (y\wedge z)=(x\vee y)\wedge(x\vee z)$

Remark: Click on the 'Edit text of this page' link at the bottom to add some information about complete distributive lattices

It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.

##### Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be … . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$

### Definition

An is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that

$...$ is …: $axiom$

$...$ is …: $axiom$

Example 1:

### Properties

Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.

Classtype second-order

### Subclasses

[[...]] subvariety
[[...]] expansion

### Superclasses

[[...]] supervariety
[[...]] subreduct
##### Toolbox 