On modified Reedy and modified projective model structures.

Johnson, Mark W.

Displaying similar documents to “On modified Reedy and modified projective model structures.”

Closed model categories for $[n, m,]$ -types.

Extremiana Aldana, J.Ignazio, Hernández Paricio, L.Javier, Rivas Rodríguez, M.Teresa (1997)

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Model structures for homotopy of internal categories.

Everaert, T., Kieboom, R.W., Van der Linden, T. (2005)

Theory and Applications of Categories [electronic only]

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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...

Quillen's theory for algebraic models of n-types.

J. G. Cabello, A. R. Garzón (1994)

Extracta Mathematicae

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Generalized Brown representability in homotopy categories.

Rosický, Jiří (2005)

Theory and Applications of Categories [electronic only]

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Localization of $𝒱$ -categories.

Dundas, Bjørn Ian (2001)

Theory and Applications of Categories [electronic only]

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Algebraic model structures.

Riehl, Emily (2011)

The New York Journal of Mathematics [electronic only]

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The shape of a category up to directed homotopy.

Grandis, Marco (2005)

Theory and Applications of Categories [electronic only]

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Simplicial and categorical diagrams, and their equivariant applications.

Fritsch, Rudolf, Golasiński, Marek (1998)

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Coherent categories with respect to monads and coherent prohomotopy theory

M. A. Batanin (1993)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Quotient models of a category up to directed homotopy.

Grandis, Marco (2006)

Theory and Applications of Categories [electronic only]

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Homotopy-theoretic aspects of 2-monads.

Lack, S. (2007)

Journal of Homotopy and Related Structures

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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. ...