Consider this context from wikipedia:
It is known that a chain map $f_\bullet$ between chain complexes $(A_\bullet, d_{A,\bullet})$ and $(B_\bullet, d_{B,\bullet})$ induces a homomorphism $$(f_\bullet)_*: H_\bullet(A_\bullet)\to H_\bullet(B_\bullet).$$
(https://en.wikipedia.org/wiki/Chain_complex#Chain_maps)
I am confused about the notation $(f_\bullet)_*: H_\bullet(A_\bullet)\to H_\bullet(B_\bullet).$
Does it mean: $(f_n)_*: H_n(A_\bullet)\to H_n(B_\bullet)$, for each $n$? (in this case the bullets are different).
If we require the bullets to be the same, then $(f_n)_*: H_n(A_n)\to H_n(B_n)$ does not seem to make sense as Homology is defined for a chain complex, not for a single group in the chain?
In general, for this kind of notation, do we need $\bullet$ to be the same thing in the same equation?