相干上链复形和Beilinson t结构，附Achim Krause附录
Coherent cochain complexes and Beilinson t-structures, with an appendix by Achim Krause
摘要：
我们定义和研究相干上链复形在任意稳定的$\infty$范畴，Joyal。我们的主要结果是：稳定的$\infty$-范畴$\mathscr C$中的凝聚上链复形的$\infty$ -范畴等价于$\mathscr C$中的完全过滤对象的$\infty$ -范畴.然后，我们将展示如何贝林森t-结构可以解释在这种等价性，并分析其行为的存在下，对称monoidal结构。我们还研究了（高）户田括号和连贯的上链复形的概念之间的关系。最后，我们证明了每一个相干的上链复形如何产生一个谱序列，并举例说明。
英文摘要：
We define and study coherent cochain complexes in arbitrary stable $\infty$-categories, following Joyal. Our main result is that the $\infty$-category of coherent cochain complexes in a stable $\infty$-category $\mathscr C$ is equivalent to the $\infty$-category of complete filtered objects in $\mathscr C$. We then show how the Beilinson t-structure can be interpreted in light of such equivalence, and analyze its behavior in the presence of symmetric monoidal structures. We also examine the relationship between the notion of (higher) Toda brackets and coherent cochain complexes. Finally, we prove how every coherent cochain complex gives rise to a spectral sequence and illustrate some examples.
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