categories names the groups along the x-axis; a_values and b_values hold one value each per category.

Draw the two series side by side within each category: positions 0, 1, 2, ... for the categories, bars of width 0.4, series A centred half a bar-width left of each position and series B half a bar-width right. Label them "A" and "B" and show the legend.

Return the Axes. Side by side, not stacked: each pair of bars shares a category but neither sits on top of the other.