orderhomomorphism
nounUK /ˈɔːdəˌhɒməˈmɔːfɪzəm/
US /ˈɔːrdərˌhoʊməˈmɔːrfɪzəm/
A way to match two ordered sets so the order stays the same.
The map from small numbers to big numbers is an order homomorphism because it keeps everything in line.
OTHER MEANINGS
2. In lattice theory, a map that preserves both joins and meets.
A lattice homomorphism is a special order homomorphism that also respects joins and meets.
3. A function between ordered sets where x ≤ y implies f(x) ≤ f(y).
Every increasing function on the real line is an order homomorphism.
4. A structure-preserving map between preordered sets.
The quotient map is an order homomorphism from the preorder to its quotient.