Are the inequalities reversed in the following statements?

> "It's worth noting a little spinoff of the argument I gave. If \$$f : A \to B \$$ is _any_ monotone function between posets,
>
> $$f(a \vee a') \le f(a) \vee f(a')$$
>
> when the joins here actually exist. Assuming that \$$f \$$ is a left adjoint gives us the reverse inequality.
> Similarly, if \$$g : B \to A \$$ is any monotone function between posets,
>
> $$g(b \wedge g') \ge g(b) \wedge g(b')$$
>

Because \$$a \vee a' \ge a \$$ and \$$a \vee a' \ge a' \$$, therefore \$$f(a \vee a') \ge f(a) \$$ and \$$f(a \vee a') \ge f(a') \$$ .