#
The two out of three property in ind-categories and a convenient model
category of spaces

##
Ilan Barnea

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.

Keywords:
Ind-categories, model categories, cofibration categories, simplicially
enriched categories, compact Hausdorff spaces

2010 MSC:
55U35, 55P05, 55U10, 54B30, 18G55, 18B30, 18C35, 18D20

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 17, pp 620-651.

Published 2017-04-28.

http://www.tac.mta.ca/tac/volumes/32/17/32-17.pdf

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