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Feb 6, 2016 at 9:07 comment added Jiří Rosický This is a special case of Remark 5.33 in my book with Adámek which deals with small cone injectivity.
Feb 3, 2016 at 13:38 comment added Peter LeFanu Lumsdaine @ZhenLin: ah, thankyou! Henrik Forssell also pointed out to me that the same converse appears in the Adamek/Rosicky book, in the hint to Exercise 5.e. These would be close enough to serve as a reference if there’s nothing closer, but it would be nice to have this version itself if it’s been set down somewhere.
Feb 3, 2016 at 12:45 comment added Zhen Lin I've used the converse of this – that injectivity conditions are regular sequents – in my paper on internal homotopy theory.
Feb 3, 2016 at 12:39 history edited Peter LeFanu Lumsdaine CC BY-SA 3.0
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Feb 3, 2016 at 12:30 history asked Peter LeFanu Lumsdaine CC BY-SA 3.0