We show that operadic categories and Feynman categories have unusual but useful relationships.
More specifically we will discuss three results about these categories which in a sense determine each other:
1. Feynman categories Fey form a full reflective subcategory of operadic categories Oper.
2. There are two other functors: O: Fey → Oper, F:Oper → Fey with the property that the composites F(O) and O(F) are +-constructions on corresponding categories.
3. Both Fey and Oper are equipped with comprehensive factorisation systems which are consistent with the above functors in appropriate sense.