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Summary: Weak factorization systems and
topological functors
Ji r Ad amek 1 , Horst Herrlich, Ji r Rosick y 2 , and Walter Tholen 3
A ectionately dedicated to Heinrich Kleisli who gave us the Kleisli{construction
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Abstract
Weak factorization systems, important in homotopy theory, are related to
injective objects in comma{categories. Our main result is that full functors
and topological functors form a weak factorization system in the category of
small categories, and that this is not co brantly generated. We also present a
weak factorization system on the category of posets which is not co brantly
generated. No such weak factorization systems were known until recently.
This answers an open problem posed by M. Hovey.
Mathematics Subject Classi cations (2000): 18A22, 18A32, 18G05,
18B35.
Key words: Weak factorization systems, full functor, topological functor,
co brantly generated, poset.
Introduction
Whereas factorization systems for morphisms in categories are one of the most stud-
ied categorical concepts, weak factorization systems have been rather neglected, al-
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