Category:Definitions/Lattices (Order Theory)

This category contains definitions related to lattices in the context of order theory.
Related results can be found in Category: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.