Lax orthogonal factorisation systems

作者：Clementino Maria Manuel; Franco Ignacio Lopez^*

来源：Advances in Mathematics, 2016, 302: 458-528.

DOI：10.1016/j.aim.2016.07.028

• Lax idempotent algebraic weak factorisation system
• Algebraic weak factorisation system
• Weak factorisation system
• Lax idempotent 2-monad
• Simple reflection

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, Hebert 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.

• 出版日期2016-10-22