Kerodon

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

Definition 4.4.2.6. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. We will say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is conservative if it satisfies the following condition:

  • Let $u: X \rightarrow Y$ be a morphism in $\operatorname{\mathcal{C}}$. If $F(u): F(X) \rightarrow F(Y)$ is an isomorphism in the $\infty $-category $\operatorname{\mathcal{D}}$, then $u$ is an isomorphism.