Lax正交分解系统
Lax orthogonal factorisation systems
摘要：
本文引入了2-范畴上的松弛正交代数弱因子分解系统，并给出了它们的构造方法。这种方法基于简单2-单子的概念，这是卡西迪，赫伯特和凯利研究的简单反射的概括。一个完备2-范畴上的每一个单2-单子都产生一个松弛正交代数弱因子分解系统，并给出了一类上极限下的完备化单2-单子的一个例子。研究了KZ提升运算、松弛自然提升运算和态射之间的松弛正交性等概念。
英文摘要：
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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