# Kerodon

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Remark 4.2.3.6. Suppose we are given a pullback diagram of categories

$\xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}' \ar [r] \ar [d]^-{U'} & \operatorname{\mathcal{E}}\ar [d]^-{U} \\ \operatorname{\mathcal{C}}' \ar [r] & \operatorname{\mathcal{C}}. }$

If $U$ is a left covering functor, then $U'$ is a left covering functor. If $U$ is a right covering functor, then $U'$ is a right covering functor.