Geodesic
The two out of three property in ind-categories and a convenient model category of spaces
Theory and applications of categories, Tome 32 (2017), pp. 620-651

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The author and Tomer Schlank studied a much weaker homotopical structure than a model category, which we called a "weak cofibration category". We showed that a small weak cofibration category induces in a natural way a model category structure on its ind-category, provided the ind-category satisfies a certain two out of three property. The main purpose of this paper is to give sufficient intrinsic conditions on a weak cofibration category for this two out of three property to hold. We consider an application to the category of compact metrizable spaces, and thus obtain a model structure on its ind-category. This model structure is defined on a category that is closely related to a category of topological spaces and has many convenient formal properties. A more general application of these results, to the (opposite) category of separable $C^*$-algebras, appears in a paper by the author, Michael Joachim and Snigdhayan Mahanta.

Publié le :
Classification : 55U35, 55P05, 55U10, 54B30, 18G55, 18B30, 18C35, 18D20
Keywords: Ind-categories, model categories, cofibration categories, simplicially enriched categories, compact Hausdorff spaces 
@article{TAC_2017_32_a16,
     author = {Ilan Barnea},
     title = {The two out of three property in ind-categories and a convenient model
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     journal = {Theory and applications of categories},
     pages = {620--651},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a16/}
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Ilan Barnea. The two out of three property in ind-categories and a convenient model
category of spaces. Theory and applications of categories, Tome 32 (2017), pp. 620-651. http://geodesic.mathdoc.fr/item/TAC_2017_32_a16/