Six operations formalism for generalized operads

Abstract

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.

final version with minor corrections, most notably revised statement of Theorem 6.3

Cited by in corpus (4)

• Dwyer--Kan homotopy theory for cyclic operads
• Coextension of scalars in operad theory
• Differential forms on smooth operadic algebras
• Toward a minimal model for $H_{\ast }(\overline{\mathcal{M}})$