Operads, operadic categories and the blob complex
Michael Batanin, Martin Markl
TL;DR
This paper links the Morrison-Walker blob complex in Topological Quantum Field Theory to an operadic bar resolution, introduces unary operadic categories, and explores new phenomena in this framework.
Contribution
It establishes a connection between the blob complex and operadic bar resolutions and develops the theory of unary operadic categories with novel phenomena.
Findings
Blob complex is an operadic bar resolution of a specific operad.
Development of unary operadic categories.
Discovery of new phenomena in operadic categories.
Abstract
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 relations. As a by-product we develop the theory of unary operadic categories and study some novel and interesting phenomena arising in this context.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra