Lax orthogonal factorisation systems

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• 作者：Maria Manuel Clementino^a ; ^{mmc@mat.uc.pt" class="auth_mail" title="E-mail the corresponding author} ; Ignacio Ló ; pez Franco^b ; ¹ ; ^{ill20@cam.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 18D05 ; 18A32 ; secondary ; 55U35
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：22 October 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：458-528
• 全文大小：1048 K

文摘

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.