A non-crossing word cooperad for free homotopy probability theory
Gabriel C. Drummond-Cole
TL;DR
This paper introduces a new cooperad that extends homotopy probability theory to free probability, potentially linking it to known operads like sequence and cactus operads, and offering new tools for the field.
Contribution
The authors construct a novel cooperad that bridges homotopy probability theory and free probability, expanding the theoretical framework.
Findings
Constructed a cooperad extending homotopy probability to free probability
Identified connections to sequence and cactus operads
Potential for independent interest in operad theory
Abstract
We construct a cooperad which extends the framework of homotopy probability theory to free probability theory. The cooperad constructed, which seems related to the sequence and cactus operads, may be of independent interest.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra