A Quillen adjunction between algebras and operads, Koszul duality, and the Lagrange inversion formula
Category Theory
2020-10-15 v1 Combinatorics
K-Theory and Homology
Abstract
We define, for a somewhat standard forgetful functor from nonsymmetric operads to weight graded associative algebras, two functorial "enveloping operad" functors, the right inverse and the left adjoint of the forgetful functor. Those functors turn out to be related by operadic Koszul duality, and that relationship can be utilised to provide examples showing limitations of two standard tools of the Koszul duality theory. We also apply these functors to get a homotopical algebra proof of the Lagrange inversion formula.
Cite
@article{arxiv.1606.08222,
title = {A Quillen adjunction between algebras and operads, Koszul duality, and the Lagrange inversion formula},
author = {Vladimir Dotsenko},
journal= {arXiv preprint arXiv:1606.08222},
year = {2020}
}
Comments
11 pages, comments are welcome