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Lax orthogonal factorisation systems

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arxiv 1503.06469 v2 pith:Y2LGY6B2 submitted 2015-03-22 math.CT math.AT

Maria Manuel Clementino , Ignacio Lopez Franco This is my paper · ORCID
classification math.CTmath.AT
keywords simplefactorisationmonadorthogonalalgebraicliftingmethodoperation
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This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.

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  1. From Grothendieck cofibrations to factorization systems: a formal 2-monadic account

    math.CT 2026-07 accept novelty 6.0 of 10

    Transport along a cofibration is converted, by a change of 2-monads, into the cocartesian–vertical factorization of arrows in the total category.

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