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Let $X$ be a complex variety equipped with a stratification. Let us assume, that all strata are contractible and in addition, that all strata closures are smooth.

Is there an "easy" quiver description of the category of perverse sheaves in this case?

For example does this category only depend on the poset of strata?

This sounds too optimistic, so what additional information is needed?

For example if we are also given the conormal bundles of the strata closures, can one reconstruct the category from this data?

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