# Extension-closed subcategory $P(I)$ defined by stability condition $(Z, P)$ and an interval $I \subset \mathbb{R}$

Let $$D$$ be a triangulated category, and let $$\sigma = (Z, P)$$ be a Bridgeland stability condition on $$D$$. Let $$I \subset \mathbb{R}$$ be any interval (open, closed, or half-open).

The category $$P(I)$$ is defined to be the extension closed subcategory generated by $$P(\phi)$$ for all $$\phi \in I$$. Bridgeland claims that if $$I = (a,b)$$, then $$P(I)$$ consists of all objects $$E$$ with $$a < \phi^-(E) \leq \phi^+(E) < b. \tag{*}$$

Q: Why does $$(*)$$ define an extension closed subcategory? For example if $$a < \phi < \psi < \phi + 1 < b,$$ one could have a triangle $$A \to B \to C \to A[1]$$ where $$A \in P(\phi)$$ and $$C \in P(\psi)$$. Then I don't see how the Harder-Narasimhan-filtration of $$B$$ looks like.