Comparing Feynman and Operadic categories
Michael Batanin – 11 December 2019
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.