The Stacks project

Lemma 4.24.6. Let $u$ be a left adjoint of $v$ as in Definition 4.24.1.

  1. If $\mathcal{C}$ has finite colimits, then $u$ is right exact.

  2. If $\mathcal{D}$ has finite limits, then $v$ is left exact.

Proof. Obvious from the definitions and Lemma 4.24.5. $\square$

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