Lax orthogonal factorisation systems
Category Theory
2016-09-13 v2 Algebraic Topology
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, 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.
Cite
@article{arxiv.1503.06469,
title = {Lax orthogonal factorisation systems},
author = {Maria Manuel Clementino and Ignacio Lopez Franco},
journal= {arXiv preprint arXiv:1503.06469},
year = {2016}
}
Comments
59 pages