We give an explicit handy (and cocycle-free) description of the groupoid of
weak maps between two crossed-modules using what we call a {\em papillon};
Theorem 8.3. We define composition of papillons and this way find a bicategory
that is naturally biequivalent to the 2-category of pointed homotopy 2-types.
This has applications in the the study of 2-group actions (say, on stacks).
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