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.