The universal simplicial bundle is a simplicial group

TL;DR

This paper demonstrates that the classical universal bundle functor for simplicial groups can be extended to a monad, and this extension applies broadly to simplicial algebras for Lawvere theories containing groups.

Contribution

It extends the universal bundle functor to a monad on simplicial groups and generalizes this to simplicial algebras for Lawvere theories.

Findings

The universal bundle functor lifts to a monad on sGrp(C).

Extension to simplicial algebras for Lawvere theories.

Broad applicability in categorical algebra.

Abstract

The classical universal bundle functor W:sGrp(C) \to sSet(C) for simplicial groups in a category C with finite products lifts to a monad on sGrp(C). This result extends to simplicial algebras for any Lawvere theory containing that of groups.