E-infinity structures over L-algebras

TL;DR

This paper introduces L-algebras as a generalization of certain chain complex structures and demonstrates they possess an E-infinity coalgebra structure, offering new tools for studying homotopy types.

Contribution

It establishes that L-algebras naturally carry an E-infinity coalgebra structure, expanding the framework for analyzing homotopy-theoretic properties.

Findings

L-algebras generalize structures from chain complexes.

L-algebras have an E-infinity coalgebra structure.

L-algebras encode significant homotopy information.

Abstract

In this paper we introduce the concept of L-algebras, which can be seen as a generalization of the structure determined by the Eilenberg-Mac lane transformation and Alexander-Whitney diagonal in chain complexes. In this sense, our main result states that L-algebras are endowed with an E-infinity coalgebra struture, like the one determined by the Barrat-Eccles operad in chain complexes. This results implies that the canonical L-algebra of spaces contains as much homotopy information as its usually associated E-infinity coalgebras, suggesting L-algebras as a tool for the study of homotopy types.