Koszul duality for operadic categories

Abstract

The aim of this sequel to arXiv:1812.02935 is to set up the cornerstones of Koszul duality and Koszulity in the context of operads over a large class of operadic categories. In particular, for these operadic categories we will study concrete examples of binary quadratic operads, describe their Koszul duals and prove that they are Koszul. This includes operads whose algebras are the most important operad- and PROP-like structures such as the classical operads, their variants such as cyclic, modular or wheeled operads, and also diverse versions of PROPs such as properads, dioperads, 1/2PROPs, and still more exotic objects such as permutads and pre-permutads.

arXiv comment56 pages. Final version. arXiv admin note: substantial text overlap with arXiv:1812.02935

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Cited by in corpus (5)

• Deformation theory of Cohomological Field Theories
• Operadic categories as a natural environment for Koszul duality
• The incidence comodule bialgebra of the Baez-Dolan construction
• Categories of graphs for operadic structures
• Combinatorial homotopy theory for operads