Motivic functors.
Dundas, Bjørn Ian, Röndigs, Oliver, Østvær, Paul Arne (2003)
Documenta Mathematica
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Dundas, Bjørn Ian, Röndigs, Oliver, Østvær, Paul Arne (2003)
Documenta Mathematica
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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...
Bousfield, A.K. (2003)
Geometry & Topology
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Jerome William Hoffman (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Levine, Marc (2007)
Documenta Mathematica
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Rosický, Jiří (2005)
Theory and Applications of Categories [electronic only]
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Thomason, R.W. (1995)
Theory and Applications of Categories [electronic only]
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Murray Heggie (1992)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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J. García-Calcines, P. García-Díaz, S. Rodríguez-Machín (2006)
Open Mathematics
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Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids. ...
Christensen, J.Daniel, Isaksen, Daniel C. (2004)
Algebraic & Geometric Topology
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