|Endomorphisms of the semigroup of order-preserving mappings
Fernandes, Vítor Hugo; Jesus, Manuel M.; Maltcev, Victor; Mitchell, James D.
Semigroup Forum, 81 (2010), 277-285
We characterize the endomorphisms of the semigroup of all order-preserving mappings on a finite chain. We show that there are three types of endomorphism: automorphisms, constants, and a certain type of endomorphism with two idempotents in the image.