  In 1984, Charney and Lee defined a category of stable curves and exhibited a
rational homology equivalence from its geometric realisation to (the
analytification of) the moduli stack of stable curves, also known as the
Deligne-Mumford-Knudsen compactification. We strengthen this result by showing
that, in fact, this category captures the stratified homotopy type of the
moduli stack. In particular, it classifies constructible sheaves via an
exodromy equivalence.
