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

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

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

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

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

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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