Abstract
In a system of interlocking sequences, the assumption that three
out of the four sequences are exact does not guarantee the
exactness of the fourth. In 1967, Hilton proved that,
with the additional condition that it is differential at the
crossing points, the fourth sequence is also exact. In this paper,
we trace such a diagram and analyze the relation between the
kernels and the images, in the case that the fourth sequence is
not necessarily exact. Regarding the exactness of the fourth
sequence, we remark that the exactness of the other three
sequences does guarantee the exactness of the fourth at
noncrossing points. As to a crossing point