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Mar 7, 2013 at 19:26 history edited David White CC BY-SA 3.0
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Mar 7, 2013 at 15:22 comment added Philippe Gaucher The paper you mention even gives the answer: top of page 24 : "We should remark that any locally presentable topologically bicomplete category also satisfies our hypothesis". And as far as I can understand the paper, any convenient category of topological spaces is fine, by convenient it is meant cartesian closed and containing enough topological spaces (e.g. CW-complexes).
Mar 7, 2013 at 15:17 vote accept Philippe Gaucher
Mar 7, 2013 at 13:28 history answered David White CC BY-SA 3.0