55 citations · 264 across the 53 of their papers we have counts for
5 papers · 1 filter
Operads, operadic categories and the blob complex
Michael Batanin, Martin Markl
We will show that the Morrison-Walker blob complex appearing in Topological Quantum Field Theory is an operadic bar resolution of a certain operad composed of fields and local rela…
Koszul duality for operadic categories
Michael Batanin, Martin Markl
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 par…
Minimal models for graph-related (hyper)operads
Michael Batanin, Martin Markl, Jovana Obradović
We construct explicit minimal models for the (hyper)operads governing modular, cyclic and ordinary operads, and wheeled properads, respectively. Algebras for these models are homot…
Permutads via operadic categories, and the hidden associahedron
Martin Markl
The present article exploits the fact that permutads (aka shuffle algebras) are algebras over a terminal operad in a certain operadic category Per. In the first, classical part we…
Operadic categories as a natural environment for Koszul duality
Michael Batanin, Martin Markl
This is the first paper of a series which aims to set up the cornerstones of Koszul duality for operads over operadic categories. To this end we single out additional properties of…