On sheet A I have an accounting-style worksheet with the category heading in
bold (column A) and then the list of itemized expenses with a total at the
bottom (labels in column A, figures in column B.) Then another category
follows laid out the same way and another, etc.

On sheet B I have a list of all the category names next to which I need to
show the totals of each category (from sheet A.) I assume a lookup function
or functions would be used but I don't know how to structure the formula to
match on the category name in sheet A and then follow down to the total row
and return the total figure in the cell in column B.