Kerodon

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

Remark 1.2.4.5. Let $\operatorname{\mathcal{C}}$ be a category. The core $\operatorname{\mathcal{C}}^{\simeq }$ is determined (up to isomorphism) by the following properties:

  • The category $\operatorname{\mathcal{C}}^{\simeq }$ is a groupoid.

  • If $\operatorname{\mathcal{D}}$ is a groupoid, then every functor $F: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ factors (uniquely) through $\operatorname{\mathcal{C}}^{\simeq }$.