Weak cofibrations in categories of cofibrant objects.
Kieboom, R.W., Sonck, G., Van der Linden, T., Witbooi, P.J. (2003)
Homology, Homotopy and Applications
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Displaying similar documents to “A category model proof of the cogluing theorem”
Weak cofibrations in categories of cofibrant objects.
Heller's axioms for homotopy theory
Jerome William Hoffman (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Abstract homotopy theory in procategories
Timothy Porter (1976)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Quillen's theory for algebraic models of n-types.
J. G. Cabello, A. R. Garzón (1994)
Extracta Mathematicae
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Homotopy colimits in presheaf categories
Murray Heggie (1993)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Inverting weak dihomotopy equivalence using homotopy continuous flow.
Gaucher, Philippe (2006)
Theory and Applications of Categories [electronic only]
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Cat as a closed model category
R. W. Thomason (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Stratified model categories
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...
Non functorial cylinders in a model category
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. ...
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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