Lusternik-Schnirelmann-categorical sections
Octavian Cornea (1995)
Annales scientifiques de l'École Normale Supérieure
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Octavian Cornea (1995)
Annales scientifiques de l'École Normale Supérieure
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Francisco Díaz, Sergio Rodríguez-Machín (2006)
Open Mathematics
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Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples...
Takahisa Miyata (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the...
Michael A. Mandell (2006)
Publications Mathématiques de l'IHÉS
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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E algebras is faithful but not full.
Peter I. Booth (1998)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Grandis, Marco (2002)
Theory and Applications of Categories [electronic only]
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Floris Takens (1970)
Compositio Mathematica
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Murray Heggie (1992)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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J. Remedios-Gómez, S. Rodríguez-Machín (2001)
Extracta Mathematicae
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