Using Escardó’s characterization of injectivity via Kock–Zöberleinmonads, we introduce suitable monads in comma categories of topological spaces that yield characterizations of fibrewiseinjectivity 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.

Fibrewise injectivity and Kock-Zöberlein monads / F.Cagliari, M. M. Clementino, S. Mantovani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 216:11(2012 Nov), pp. 2411-2424.

Fibrewise injectivity and Kock-Zöberlein monads

S. Mantovani
Ultimo
2012

Abstract

Using Escardó’s characterization of injectivity via Kock–Zöberleinmonads, we introduce suitable monads in comma categories of topological spaces that yield characterizations of fibrewiseinjectivity 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.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
nov-2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/178621
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