A combinatorial PROP for bialgebras
Jorge Becerra
TL;DR
This paper constructs an extended PROP for bialgebras by attaching permutations to the classical PROP for commutative bialgebras, providing a new categorical framework.
Contribution
It introduces a novel extension of the classical PROP for commutative bialgebras that incorporates permutations to model non-commutative structures.
Findings
Extended PROP is equivalent to the PROP for bialgebras
Provides a categorical framework for non-commutative bialgebras
Links permutations with algebraic operations in bialgebras
Abstract
It is a classical result that the category of finitely-generated free monoids serves as a PROP for commutative bialgebras. Attaching permutations to fix the order of multiplication, we construct an extension of this category that is equivalent to the PROP for bialgebras.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology