Is my understanding of the process of charging a capacitor correct?

Suppose, I have a parallel plate capacitor with copper plates $A$ & $B$ connected to a battery. Plate A is connected to the negative terminal of the battery and plate B is connected to the positive terminal.

Now, due to the reducing agent present in the negative terminal of the battery, copper atoms of terminal A get reduced; so, a net negative charge is formed in plate A. Furthermore, due to the oxidizing agent present in the positive terminal of the battery, copper atoms of plate B get oxidized, forming a net positive charge.

But the amount of charge formed in plate $A$ & $B$ is found to be equal. This is because the net charge of the capacitor tends to stay zero; i.e., the capacitor tends to have has no net charge. This is why the amount of charge formed in plate $A$ & $B$ is found to be equal.

This is my understanding of how a capacitor is charged. Is it accurate?