Category with a natural cone

Francisco Díaz; Sergio Rodríguez-Machín

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Homotopy theory for (braided) cat-groups

Antonio R. Garzon, Jesus G. Miranda (1997)

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Homotopy cofibrations in $C A T$

Murray Heggie (1992)

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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. ...