Faithful highest weight hearts equal serially faithful glued hearts with dual exceptional collections; faithful perverse categories on finite-strata spaces have global dimension at most dim(X), with hypercohomology computable from constant sheaf resolutions via intersection cohomology.
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Faithful perversities
Faithful highest weight hearts equal serially faithful glued hearts with dual exceptional collections; faithful perverse categories on finite-strata spaces have global dimension at most dim(X), with hypercohomology computable from constant sheaf resolutions via intersection cohomology.