Weak reflections and weak factorization systems

Authors

Michel Hébert, American University in CairoFollow

Author's Department

Mathematics & Actuarial Science Department

Find in your Library

https://doi.org/10.1007/s10485-008-9164-1

Document Type

Research Article

Publication Title

Applied Categorical Structures

Publication Date

1-1-2011

doi

10.1007/s10485-008-9164-1

Abstract

We describe a one-to-one correspondence between saturated weak factorization systems and weak reflections in categories C with finite products. This actually extends to an adjunction between the category of natural weak factorization systems on C (in the sense of Grandis and Tholen, Arch Math 42:397-408, 2006, and Garner, arXiv preprint, 2007) and the category of monads on C . Explicit comparisons are made with the parallel result of Cassidy et al. (J Aust Math Soc 38:287-329, 1985), linking factorization systems and reflective subcategories. © 2008 Springer Science+Business Media B.V.

First Page

9

Last Page

38

Recommended Citation

APA Citation

Hébert, M. (2011). Weak reflections and weak factorization systems. Applied Categorical Structures, 19(1), 9–38. 10.1007/s10485-008-9164-1
https://fount.aucegypt.edu/faculty_journal_articles/689

MLA Citation

Hébert, Michel "Weak reflections and weak factorization systems." Applied Categorical Structures, vol. 19,no. 1, 2011, pp. 9–38.
https://fount.aucegypt.edu/faculty_journal_articles/689