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$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Proposition 10.2.2.14. The diagram of $\infty $-categories

\[ \xymatrix@R =50pt@C=50pt{ \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\operatorname{inj}} ) \ar [r] \ar [d] & \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}) \ar [d] \\ \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\operatorname{inj}, +} ) \ar [r] & \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{+} ) } \]

is a categorical pushout square.

Proof. By virtue of Proposition 7.2.2.1, this is a reformulation of Proposition 10.2.2.6. $\square$