Corrigendum to "Unifying derived deformation theories" [Adv. Math. 224 (3) (2010) 772-826]
Corrigendum to "Unifying derived deformation theories" [Adv. Math. 224 (3) (2010) 772-826]
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“统一派生变形理论”的勘误表 [Adv.
DOI：
10.1016/j.aim.2011.07.004
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发表时间：
2011
影响因子：
1.7
通讯作者：
Pridham J
中科院分区：
文献类型：
--
作者：
Pridham J
定义2.7和4.11中几何弱等价的定义是不正确的。事实上，取p为B上的恒等态射，则给出的定义等价于同构。因此，在引理2.10的证明的最后一行中有一个错误，所以引理中的“if”蕴涵是假的;这影响了定理2.10的证明。相关定义应修改如下。
The definition of geometric weak equivalences in Definitions 2.7 and 4.11 is incorrect. In fact, taking p to be the identity morphism on B, it follows that the definition given is equivalent to being an isomorphism. There is consequently an error in the final line of the proof of Lemma 2.10, so the “if” implication in the lemma is false as stated; this affects the proof of Theorem 2.10. The relevant definitions should be modified as follows.