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arXiv · 1503.06469

Lax orthogonal factorisation systems

Maria Manuel Clementino·Ignacio Lopez Franco
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Abstract

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, Hébert 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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Maria Manuel Clementino, Ignacio Lopez Franco. 2016-09-09. Lax orthogonal factorisation systems. https://doi.org/10.1016/j.aim.2016.07.028

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