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DerivedAlgGeo.CategoryTheory.Abelian.Stability.Weak

Weak stability functions on an abelian category #

The weakened variant of the theory its parent directory owns: the charge is allowed to land on 0, so the slope takes values in WithTop ℝ and a zero-charge object is not excluded from the subobject quantifier. Everything here is a variant of a neighbour one level up, which is why it is a child and not a sibling -- MetricSpace/Pseudo/ in Mathlib names the same relationship.

The dependency runs the other way, as it does there. Stability/Slope.lean imports Weak/Slope.lean and adds the strict positivity that rules ⊤ out; Stability/PhaseMonotone.lean and the Uniqueness/ files are shared by both. Directory nesting names the variant, not the import direction.

Why this is not below Triangulated/ #

Nothing in this subtree mentions a shift, a distinguished triangle, a t-structure or a heart. It asks for an abelian category, an additive charge out of its Grothendieck group, and a half-plane. Until MO1.08 (#1319) it lived below Triangulated/StabilityCondition/Weak/Foundation/, where the subject it is a foundation for owned it; the triangulated weak theory now consumes it across the CategoryTheory/Abelian/ boundary like any other client.

Declaration namespaces are unchanged and remain CategoryTheory.Triangulated; see decision 1 of the MO1 owner map in docs/architecture/cutover-ledger.md.