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May 6, 2017 at 13:06 vote accept user316092
May 6, 2017 at 12:36 comment added Tim Porter Have a look at some of the books on Quillen's theory. On fibrant-cofibrant objects a weak equivalence has a homotopy inverse with homotopy given by a cylinder or cocylinder object (I paraphrase a bit here.) Your question is not quite well posed, as it is not clear what `coincide' refers to.
May 6, 2017 at 11:55 comment added user316092 Ah I see, thanks. Do weak equivalences always coincide on the class of cofibrant-fibrant objects?
May 6, 2017 at 11:52 history edited Tim Porter CC BY-SA 3.0
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May 5, 2017 at 14:23 history answered Tim Porter CC BY-SA 3.0