An orthogonal approach to algebraic weak factorisation systems

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.

Added intro to double categories and discussion of homotopical examples. Journal version

References in corpus (3)

• Algebraic weak factorisation systems I: accessible AWFS
• The Frobenius Condition, Right Properness, and Uniform Fibrations
• The Coalgebraic Structure of Cell Complexes