The Stacks project

Remark 13.33.3. Let $\mathcal{D}$ be a triangulated category. Let $(a_ n) : (K_ n, f_ n) \to (L_ n, g_ n)$ be a morphism of systems of objects of $\mathcal{D}$. Let $(K, i_ n, c)$ be a derived colimit of the first system and let $(L, j_ n, d)$ be a derived colimit of the second system with notation as in Remark 13.33.2. Then there exists a morphism $a : K \to L$ such that $a \circ i_ n = j_ n$ and $d \circ a = (a_ n[1]) \circ c$. This follows from TR3 applied to the defining distinguished triangles.