Displaying similar documents to “A note on exactness and stability in homotopical algebra.”

Heaps and unpointed stable homotopy theory

Lukáš Vokřínek (2014)

Archivum Mathematicum

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In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty.

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. ...