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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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Are endofunctors of triangulated categories triangulated?

Let $\mathcal{T}$ be a triangulated category, and let $\mathcal{A}:=\operatorname{End}(\mathcal{T})$ be the category of triangulated endofunctors of $\mathcal{T}$. Is $\mathcal{A}$ triangulated? My …