This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our constructions, we prove intertwining theorems which govern derived Koszul duality of push-forwards and pull-backs.
Keywords: Operads, modular operads, graph complexes, six-operations formalism, Koszul duality
2010 MSC: 55U30,18D50
Theory and Applications of Categories, Vol. 34, 2019, No. 6, pp 121-169.