Kerodon

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

Definition 9.1.5.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, and let $f: A \rightarrow B$ and $g: X \rightarrow Y$ be morphisms of $\operatorname{\mathcal{C}}$. We will say that $f$ is weakly left orthogonal to $g$ if every lifting problem

\[ \xymatrix@C =40pt@R=40pt{ A \ar [d]^{f} \ar [r] & X \ar [d]^{g} \\ B \ar [r] \ar@ {-->}[ur] & Y } \]

in the $\infty $-category $\operatorname{\mathcal{C}}$ admits a solution. In this case, we will also say that $g$ is weakly right orthogonal to $f$.