Families of algebraic structures

TL;DR

This paper develops a comprehensive framework for understanding family algebras associated with finitely presented linear operads, linking algebraic structures to parameter spaces in a unified way.

Contribution

It introduces a general approach to family algebras over linear operads, connecting operad presentations with algebraic structures on parameter sets.

Findings

Provides a formalism for family algebras over finitely presented linear operads

Establishes a natural connection between operad presentations and parameter-based algebraic structures

Lays groundwork for further exploration of algebraic families in operad theory

Abstract

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.