What is the standard term for the property of an order-embedding $h \colon P \to P$ such that for all $a \in P$, $a \leq h(a)$?

Question

In an essay, I want to talk about order-embeddings $h \colon P \to P$ on a partially ordered set P such that

for all $a \in P$, $a \leq h(a)$.

Does somebody know the standard term for a function with that property? And also the converse ($h(a) \leq a$)? Help with maybe a reference or two would be greatly appreciated! Thank you!