
TL;DR
This paper introduces operadic torsors and quasi-torsors, demonstrating their role in establishing operad isomorphisms and providing a concise proof of the Deligne conjecture.
Contribution
It defines operadic torsors and quasi-torsors and proves their significance in determining operad isomorphisms, offering a new approach to the Deligne conjecture.
Findings
Operadic torsors imply operad (quasi-)isomorphism.
Established a shortest known proof of the Deligne conjecture.
Provided a new conceptual framework for operad equivalences.
Abstract
We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomorphic. As an application we present the (arguably) shortest known proof of the Deligne conjecture.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
