Fibrewise injectivity and Kock-Z枚berlein monads

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• 作者：Francesca Cagliari^a ; ^{cagliari@dm.unibo.it} ; Maria Manuel Clementino^b ; ^{mmc@mat.uc.pt} ; Sandra Mantovani^c ; ^{sandra.mantovani@unimi.it}
• 关键词：54C10 ; 54B30 ; 54A20 ; 18C15 ; 54F65 ; 06B35
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：November, 2012
• 卷：216
• 期：11
• 页码：2411-2424
• 文件大小：278 K

摘要

Using Escard贸鈥檚 characterization of injectivity via Kock-Z枚berlein monads, we introduce suitable monads in comma categories of topological spaces that yield characterizations of fibrewise injectivity in topological T0-spaces, with respect to the class of embeddings, and of dense, of flat and of completely flat embeddings. Characterizations, in the category of topological spaces, of injective maps with respect to the same classes of embeddings follow easily from the results obtained for T0-spaces. Moreover, it is shown that, together with the corresponding embeddings, injective continuous maps form a weak factorization system in the category of topological (T0-)spaces and continuous maps.