Closed model categories for -types.
Extremiana Aldana, J.Ignazio, Hernández Paricio, L.Javier, Rivas Rodríguez, M.Teresa (1997)
Theory and Applications of Categories [electronic only]
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Extremiana Aldana, J.Ignazio, Hernández Paricio, L.Javier, Rivas Rodríguez, M.Teresa (1997)
Theory and Applications of Categories [electronic only]
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Everaert, T., Kieboom, R.W., Van der Linden, T. (2005)
Theory and Applications of Categories [electronic only]
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Jan Spaliński (2003)
Fundamenta Mathematicae
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The fourth axiom of a model category states that given a commutative square of maps, say i: A → B, g: B → Y, f: A → X, and p: X → Y such that gi = pf, if i is a cofibration, p a fibration and either i or p is a weak equivalence, then a lifting (i.e. a map h: B → X such that ph = g and hi = f) exists. We show that for many model categories the two conditions that either i or p above is a weak equivalence can be embedded in an infinite number of conditions which imply the existence of...
J. G. Cabello, A. R. Garzón (1994)
Extracta Mathematicae
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Rosický, Jiří (2005)
Theory and Applications of Categories [electronic only]
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Dundas, Bjørn Ian (2001)
Theory and Applications of Categories [electronic only]
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Riehl, Emily (2011)
The New York Journal of Mathematics [electronic only]
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Grandis, Marco (2005)
Theory and Applications of Categories [electronic only]
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Fritsch, Rudolf, Golasiński, Marek (1998)
Theory and Applications of Categories [electronic only]
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M. A. Batanin (1993)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Grandis, Marco (2006)
Theory and Applications of Categories [electronic only]
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Lack, S. (2007)
Journal of Homotopy and Related Structures
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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. ...