  Crossed modules are known to be a model of pointed connected homotopy
2-types; formally, the homotopy category of crossed modules is equivalent to
the category of pointed connected homotopy 2-types. In forming the homotopy
category of crossed modules, one must resort to computing derived morphisms
using non-constructive topological methods, but Behrang Noohi was able to find
an algebraic model of these derived morphisms called butterflies. The result is
a completely algebraic model of pointed connected homotopy 2-types. Reduced
crossed complexes are a generalization of crossed modules and model a subclass
of pointed connected homotopy types. We will present algebraic objects called
n-butterflies which satisfy similar properties to butterflies and begin to
generalize the theory of butterflies to model morphisms of pointed connected
homotopy n-types.
