
*** nonacycl ***

This is an example of an acyclic cubical multivalued map F: X -> Y such that
its restriction to the subset A of X is not acyclic. Therefore, the map
induced by F: (X, A) -> (Y, B) cannot be computed by "homcubes".
+---+---+
| a | b |           X = Y = {a, b, c, D, e, f}      A = B = {a, b, c, e, f}
+---+---+---+
| c | D | f |       a -> {c, b}     b -> {b, f}     c -> {e, c},
*---+---+---+
    | e |           D -> {a, b, c, D, e, f}         e -> {e}       f -> {f}
    +---+
As one can analyze, the image of each elementary cube in the domain is an
acyclic set. However, if one removes the cube 'D' from the map's domain, then
the common vertex of the cubes 'a', 'b' and 'c' has the image consisting of
'b', 'c', 'e' and 'f', which is not acyclic.

Note that this map has an acyclic selector - the "orthogonal projection"
onto the stripe [0,3] x [0,1], for example (if '*' indicates the origin).
Therefore, the map induced in homology should be the identity.
