Remark 5.26 . [04G5]
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Remark 5.26.
In Definition 3.32, the Thomas-Yau semistability makes use of distinguished triangles for all almost calibrated Lagrangian objects, not just those with . This makes the Thomas-Yau semistability a priori stronger than the semistable situation of the above dichotomy. We expect from the Thomas-Yau-Joyce picture that both stability notions are actually equivalent under our initial assumption that there is a representative with . But for our main purpose, that Thomas-Yau semistability implies the existence of special Lagrangians, we do not mind Thomas-Yau semistability being stronger than necessary.