Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras

TL;DR

This paper introduces a more flexible framework for defining pseudo algebras over theories and 2-theories, correcting previous limitations and enabling better modeling of coherence diagrams.

Contribution

It generalizes the concept of pseudo algebras, addressing previous restrictions and providing a more adaptable approach for selecting coherence diagrams.

Findings

Defines a new, more flexible concept of pseudo algebras

Corrects limitations in earlier models by Hu and Kriz

Enables better representation of coherence in algebraic structures

Abstract

We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.