Weak Factorization Systems and Topological Functors |
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| Authors: | Ji?í Adámek Horst Herrlich Ji?í Rosický Walter Tholen |
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| Institution: | (1) Institut für Theoretische Informatik, Technische Universität Braunschweig, 38032 Brausnchweig, Germany;(2) Fachbereich 3, Universität Bremen, 28334 Bremen, Germany;(3) Department of Mathematics, Masaryk University, 66295 Brno, Czech Republic;(4) Department of Mathematics and Statistics, York University, Toronto, M3Y 1P3, Canada |
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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 cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey. |
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| Keywords: | weak factorization systems full functor topological functor cofibrantly generated poset |
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