natural homomorphism

The natural homomorphism $R\to R/I$ where $R$ is a ring and $I$ an ideal of $R$ is the map $\alpha \mapsto \alpha +I$. Coset operations, e.g $(\alpha +\beta )+I=(\alpha +I)+(\beta +I)$ guarantee this will be a homomorphism. Natural homomorphisms for groups can be defined similarly.