Category:Definitions/Ordered Structures

This category contains definitions related to Ordered Structures.
Related results can be found in Category:Ordered Structures.

An ordered structure $\struct {S, \circ, \preceq}$ is an algebraic system such that:

$(1): \quad \struct {S, \circ}$ is an algebraic structure

$(2): \quad \struct {S, \preceq}$ is an ordered set

$(3): \quad \preceq$ is compatible with $\circ$.