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Nov 26, 2018 at 14:57 comment added ABC The counterexample you gave is extreme :) Is there still a "reasonable" additional condition that we could impose on the functor $L$ such that under my assumptions, the functor L will takes fibrant objects to fibrant objects?
Nov 26, 2018 at 14:52 vote accept ABC
Nov 26, 2018 at 13:21 comment added David White To make the last sentence concrete, I think a counterexample $D$ is the injective model structure on $Ch(R)$ where $R$ is a self-injective ring. Or, the category of pointed simplicial sets.
Nov 26, 2018 at 13:09 history answered Reid Barton CC BY-SA 4.0