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4 votes

Does $\infty$-categorical localization commute with taking directed fibered products?

Here is a counter example in the general case: Take $E = [1] = 0 \to 1 $. $D = \{0\} \coprod \{1\} $ and $C = \{1\}$. where all maps are weak equivalence. The lax-pullback is $\{id:1 \to 1\}$, and the …
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