  One can explicitly compute the generators of a surface cluster algebra either
combinatorially, through dimer covers of snake graphs, or homologically,
through the CC-map applied to indecomposable modules over the appropriate
algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's
decorated super Teichm{\"u}ller theory to define a super version of the cluster
algebra of type $A$ and gave a combinatorial formula to compute the even
generators. We extend this theory by giving a homological way of explicitly
computing these generators by defining a super CC-map for type $A$.
