Michael Batanin ; Martin Markl - Koszul duality for operadic categories

compositionality:13523 - Compositionality, June 16, 2023, Volume 5 (2023) - https://doi.org/10.32408/compositionality-5-4
Koszul duality for operadic categoriesArticle

Authors: Michael Batanin 1; Martin Markl 2

  • 1 Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, The Czech Republic
  • 2 MFF UK, Sokolovská 83, 186 75 Prague 8, The Czech Republic

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.

https://doi.org/10.32408/compositionality-5-4
Source: arXiv.org:2105.05198
Volume: Volume 5 (2023)
Published on: June 16, 2023
Imported on: May 2, 2024
Keywords: Mathematics - Category Theory,Mathematics - Algebraic Topology
Licence: arXiv.org - Non-exclusive license to distribute
Funding:
    Source : OpenAIRE Graph
  • Enriched higher category theory; Funder: Australian Research Council (ARC); Code: DP130101172
  • Mathematical Sciences Research Institute (MSRI); Funder: National Science Foundation; Code: 1928930

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

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