Strong cofibrations and fibrations in enriched categories

Autor(en): Schwanzl, R
Vogt, RM
Stichwörter: Mathematics; SPACES
Erscheinungsdatum: 2002
Herausgeber: BIRKHAUSER VERLAG AG
Journal: ARCHIV DER MATHEMATIK
Volumen: 79
Ausgabe: 6
Startseite: 449
Seitenende: 462
Zusammenfassung: 
We define strong cofibrations and fibrations in suitably enriched categories using the relative homotopy extension resp. lifting property. We prove a general pairing result, which for topological spaces specializes to the well-known pushout-product theorem for cofibrations. Strong cofibrations and fibrations give rise to cofibration and fibration categories in the sense of homotopical algebra. We discuss various examples; in particular, we deduce that the category of chain complexes with chain equivalences and the category of categories with equivalences are symmetric monoidal proper closed model categories.
ISSN: 0003889X
DOI: 10.1007/PL00012472

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