Are there names for $A_n$, $Z_n$ and $B_n$ in a chain complex? I mean similar name like $n$-th homology group. If there would be, say "$n$-th component" for $A_n$, "The cycles of $A_n$" for $Z_n$, and "The boundaries of $A_n$" for $B_n$ than I could say that "Any cycle and boundary preserving homomorphism between the components of two chain complexes induces a homomorphism between the corresponding homology groups". What is the correct terminology for this?

If $C=(C_p)$ is a (co)cochain complex then elements in $C_p$ are usually called $p$-(co)chains. 
