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Jun 16, 2014 at 12:12 comment added Philippe Gaucher You are correct, up to weak homotopy equivalence.
Jun 16, 2014 at 10:07 comment added Zhen Lin My understanding is that the realisation of cubical sets with connection only preserves finite products up to weak homotopy equivalence. Are you saying it preserves finite products up to homeomorphism?
Jun 16, 2014 at 10:01 history answered Philippe Gaucher CC BY-SA 3.0