Let L be a non empty relational structure. Observe that every map from L into L which is kernel is also projection. Let L be a non empty reflexive relational structure. One can verify that there exists a map from L into L which is kernel. Let L be a non empty reflexive relational structure.
L is kernel.
Let L be a non empty poset, k be a map from L into L , and X be a subset of L . Observe that g is onto. If g is monotone, then g is monotone. Let L be a non empty poset and f be a map from L into L . Suppose f is a projection operator.