  Digital cubical singular homology $dH_q(X)$ for digital images $X$ was
developed by the first and third authors, and digital analogues to various
results in classical algebraic topology were proved. Another homology denoted
$H_q^{c_1}(X)$ was developed by the second author for $c_1$-digital images,
which is computationally much simpler than $dH_q(X)$. This paper shows the
functoriality of $H_q^{c_1}$, as well as a chain map between $dH_q(X)$ and
$H_q^{c_1}(X)$ when $X$ is a $c_1$-digital image.
