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Jul 25, 2018 at 18:30 comment added Harry Gindi You asked if it is true in general. It is not. I don't have a specific counterexample at the ready.
Jul 25, 2018 at 18:20 comment added tictac I do not understand your answer! if the answer is no, you need to prove the following: for a fixed fibrant object $a\in M$ there is no fibrant object $b\in N$ such that $a\rightarrow U(b)$ is an equivalence.
Jul 25, 2018 at 18:14 history answered Harry Gindi CC BY-SA 4.0