Lemma 56.4.3. With $A$, $B$, $F$, and $F'$ as in Lemma 56.4.1.

1. If $F$ is additive, then $F'$ is additive and commutes with arbitrary direct sums, and

2. if $F$ is right exact, then $F'$ is right exact.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).