Monadic Decompositions and Classical Lie Theory

TL;DR

This paper investigates the structure of bialgebras by analyzing the functor that maps a bialgebra to its primitives, revealing it has a monadic length of at most 2, which advances understanding in classical Lie theory.

Contribution

It establishes that the functor from bialgebras to vector spaces has monadic length at most 2, providing new insights into the algebraic structure related to Lie theory.

Findings

The functor from bialgebras to vector spaces has monadic length ≤ 2.

Provides a new perspective on the structure of primitives in bialgebras.

Connects monadic properties with classical Lie theory concepts.

Abstract

We show that the functor from bialgebras to vector spaces sending a bialgebra to its subspace of primitives has monadic length at most 2.