论文标题
精确$ \ infty $-类别的稳定船体
The stable hull of an exact $\infty$-category
论文作者
论文摘要
我们构造一个左伴随$ \ Mathcal {h}^\ text {st} \ colon \ mathbf {ex} _ {\ infty} \ rightArrow \ rightArrow \ MathBf {st} _ {\ infty} $ \ Mathbf {ex} _ {\ infty} $ $ \ infty $ - 稳定$ \ infty $ - 类别中的$ \ infty $ - 类别的$ \ infty $ - 类别，我们称之为稳定的船体。对于每个精确的$ \ infty $ -Category $ \ MATHCAL {E} $，单位函数$ \ Mathcal {e} \ rightArrow \ Mathcal {h}^\ text {st}（\ Mathcal {e}）$是完全忠实的，并且保存完好无损。这提供了Gabriel-Quillen嵌入普通类别的$ \ infty $分类变体。如果$ \ MATHCAL {E} $是普通的确切类别，则稳定的船体$ \ Mathcal {h}^\ text {st}（\ Mathcal {e}）$等于有限的限制的衍生的$ \ infty $ \ infty $ - 类别$ \ nathcal $ \ nathcal {e} $。
We construct a left adjoint $\mathcal{H}^\text{st}\colon \mathbf{Ex}_{\infty} \rightarrow \mathbf{St}_{\infty}$ to the inclusion $\mathbf{St}_{\infty} \hookrightarrow \mathbf{Ex}_{\infty}$ of the $\infty$-category of stable $\infty$-categories into the $\infty$-category of exact $\infty$-categories, which we call the stable hull. For every exact $\infty$-category $\mathcal{E}$, the unit functor $\mathcal{E} \rightarrow \mathcal{H}^\text{st}(\mathcal{E})$ is fully faithful and preserves and reflects exact sequences. This provides an $\infty$-categorical variant of the Gabriel-Quillen embedding for ordinary exact categories. If $\mathcal{E}$ is an ordinary exact category, the stable hull $\mathcal{H}^\text{st}(\mathcal{E})$ is equivalent to the bounded derived $\infty$-category of $\mathcal{E}$.
