Assuming we have a reaction of
$$\ce{CO2 + H2O -> HCO3- + \color{red}{H+}}$$
then is the proton (in red) is considered a product or a catalyst?
I read the Wikipedia article titled Product (chemistry), but the issue is still not clear to me. The article gives the following illustration:
In my original example above, I assume that the proton is considered a product since the hydrogen was originally part of the water molecule.
But in this case (see here, at 6:45) the hydrogen proton of the product of the reaction goes to the hemoglobin and kicks off an oxygen molecule.