A complement is a phrase whose sister is of bar level 0 and whose mother is of bar level 1. An adjunct is a phrase whose sister and mother have the same bar level. In a minimalist theory, phrase structure must adhere to the Inclusivess Condition, which requires that syntactic structures only contain material from the lexicon. Adding bar levels to a tree would involve adding something to it that is not taken from the lexicon, in violation of inclusiveness. The operation merge involves extending one of the categories involved.
Categorial projection is built into the definition of Merge and Move.