In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair (LF,RG). In particular, canonicity of this passage becomes obvious. 2nd version: added comparison to Deligne's definition (SGA4) and a discussion of diagrams of derived functors. Introduction rewritten and references added. 3rd version: description of Kan extensions in terms of correspondences more detailed. 4th version: the final version accepted to HHA.

中文翻译：

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那么，什么是派生函子呢？

在无穷范畴的背景下，我们根据对应重新思考派生函子的概念。这对于描述从函子的伴随对 (F,G) 到导出伴随对 (LF,RG) 的段落特别方便。特别是，这段经文的规范性变得明显。第二版：添加了与 Deligne 定义 (SGA4) 的比较以及对派生函子图的讨论。重写了介绍并添加了参考文献。第 3 版：根据更详细的对应关系描述 Kan 扩展。第 4 版：HHA 接受的最终版本。