Every constructible sheaf of $\mathbb{Q}$modules over $\mathbb{R}$ is the direct sum of indecomposable sheaves, which are either sheaves with stalk $\mathbb{Q}$ at a point or constant sheaves with stalk $\mathbb{Q}$ on an open interval extended by lower ! or lower * at each endpoint. What happens if we remove the 'constructible' hypothesis? Is there a similar classification?
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