Let
be a morphism
of
double groupoids
with connection. If
is thin, then
is thin.
Let
be a singular cube in a Hausdorff space
.
Then by restricting
to the faces of
and taking the
corresponding elements in
, we obtain a
cube in
which is commutative by the Homotopy
addition lemma for
([1], proposition
5.5). Consequently, if
is
a morphism of
double groupoids with connections, any singular cube
in
determines a
commutative 3-shell
in
.
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