Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Comments on Theorem 9.2.4.3

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Comment #2022 by Zhouhang Mao on

In the conclusion of the small object argument, it seems that the object is only weakly -local in place of being -local. Moreover, it seems that https://kerodon.net/tag/04MD invokes this for -localness, which seems to be strange.

Comment #2032 by Kerodon on

Thanks! The small object argument produces something weakly W-local. In the setting of Tag 04MD, we have arranged that W is closed under the formation of relative codiagonals, so this is the same as being W-local (Tag 04LY).

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