0MXQ Corollary 2.16. In the situation of Corollary 2.12 the weight complex functor induces an equivalence t:⟨𝒯⟩≅,⨭,Δ→Dperf(End𝒞(𝒯)).t:\langle\mathcal{T}\rangle_{\cong,\inplus,\Delta}\to\operatorname{D_{perf}}(\operatorname{End}_{\mathcal{C}}(\mathcal{T})). If 𝒞\mathcal{C} admits and autoequivalence ⟨1⟩\langle 1\rangle such that 𝒯^=⋃n𝒯⟨n⟩\widehat{\mathcal{T}}=\bigcup_{n}\mathcal{T}\langle n\rangle is also tilting then the weight complex functor induces an equivalence t:⟨𝒯^⟩≅,⨭,Δ→Dperfℤ(End𝒞∙(𝒯)).t:\langle\widehat{\mathcal{T}}\rangle_{\cong,\inplus,\Delta}\to\operatorname{D}^{\mathbb{Z}}_{\operatorname{perf}}(\operatorname{End}^{\bullet}_{\mathcal{C}}(\mathcal{T})).