R: Searching a column in a dataframe for matches to a reference list in another dataframe - r

Question

I am trying to categorize genes with multiple GO descriptors into bins based on what those GO descriptors are related to. I have dataframe A which contains the raw data associated with a list of geneIDs (>500,000) and their associated GO descriptors and dataframe B which classifies these GO descriptors into larger groups.
Example of dataframe A
dfA
Example of dataframe B
dfB
Ideally, the final output would reference the entire list and generate a new column in dataframe A classifying the GeneIDs into the GO_Category's associated with its specific GO_IDs -- bonus points if it removes duplicate hits on the GO_Categorys.
Looking something like this...
Example of Ideal Solution
However, I know that the ideal solution might be difficult to obtain, and I already have dataframe B listed out based on the unique GO_Categories so a solution like this might be easier to obtain.
Example of Acceptable Solution
So far I have struggled with getting any command to search for partial strings using a list from another dataframe with the goal of returning all matches.
I have had partial success with the acceptable solution approach and using:
dfA <- dfA %>%
mutate(GO_Cat_1 = c('No', 'Yes')[1+str_detect(dfA$GO_IDs, as.character(dfB$GO_IDs))])
The solution seems okay, however, it does return an error along the lines of
problem with mutate() column GO_Cat_1.
i GO_Cat_1 = ...[].
i longer object length is not a multiple of shorter object length
I have also tried to look into applying grepl/grep - but struggled to feed it a list of terms to look for partial string matches in dfA.
Any assistance is greatly appreciated!