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Let $R$ be a commutative Noetherian ring, and $D^b(\operatorname{mod } R)$ the bounded derived category of the abelian category of finitely generated $R$-modules. Let me abbreviate this as $D^b(R)$. ...

Yes, I see there are other Q&A's on this, for instance here: Projective objects in the category of chain complexes I am wondering why a level-wise projective chain complex $P$ which is split ...

Let $A$ be an abelian category (you can assume additional conditions for its goodness). Let $\mathrm{Seq}(A) = \mathrm{Func}(\mathbb{Z}, A)$, where $\mathbb{Z}$ is the standard order category on ...

Let $\mathcal{C}$ be an abelian category and $$ C_\bullet:C_n \rightarrow C_{n-1}\rightarrow \ldots \rightarrow C_1\rightarrow C_0$$ a complex in $\mathcal{C}$. Suppose we have for each $i$ a ...