Category:Lattices (Order Theory)

This category contains results about lattices in the context of order theory.
Definitions specific to this category can be found in Definitions/Lattices (Order Theory).

Let $\struct {S, \preceq}$ be an ordered set.

Suppose that $S$ admits all finite non-empty suprema and finite non-empty infima.

Denote with $\vee$ and $\wedge$ the join and meet operations on $S$, respectively.

Then the ordered structure $\struct {S, \vee, \wedge, \preceq}$ is called a lattice.