The Stacks project

Situation 22.27.2. Here $R$ is a ring and $\mathcal{A}$ is a differential graded category over $R$ having axioms (A), (B), and

  1. given an arrow $f : x \to y$ of degree $0$ with $\text{d}(f) = 0$ there exists an admissible short exact sequence $y \to c(f) \to x[1]$ in $\text{Comp}(\mathcal{A})$ such that the map $x[1] \to y[1]$ of Lemma 22.27.1 is equal to $f[1]$.

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View Situation 22.27.2 as pdf