An orthogonal approach to algebraic weak factorisation systems

TL;DR

This paper introduces an alternative formulation of algebraic weak factorisation systems using double categories and lifting operations, avoiding the traditional monad and comonad framework.

Contribution

It presents a novel, equivalent approach to algebraic weak factorisation systems that simplifies their conceptual framework by replacing monads and comonads with double categories.

Findings

Provides an equivalent formulation of algebraic weak factorisation systems.

Eliminates the need for monads and comonads in the description.

Establishes a new perspective using double categories.

Abstract

We describe an equivalent formulation of algebraic weak factorisation systems, not involving monads and comonads, but involving double categories of morphisms equipped with a lifting operation satisfying lifting and factorisation axioms.