## 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.

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