Help with a formula across multiple tabs of data

Hi there! I am trying (and failing) to write a formula that will fill in a column based on data within another tab of that same worksheet. I know it's probably super simple to do, I just can't get it to work.

First tab has transactions along with the category and a blank column that I want to fill in with the "new category".
The second tab has a list of all categories in Column A and what the "new category" should be in Column B.

Any help would be much appreciated. Thank you!