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Apr 30, 2021 at 14:46 comment added Tim Campion Nice, thanks! I think the lesson is that I probably should not have included this formulation of the question among the possible precisifications I suggested (and in particular my suspicion that "strictly injective" and "pseudo injective" might be close looks wrong now). There's a mismatch in strictness between "fully faithful" and "strictly injective". I should either ask about being strictly injective with respect to full subcategory inclusions, or ask about being pseudo-injective with respect to fully faithful functors, but I should not mix and match like this.
Apr 29, 2021 at 20:46 history answered Chris Schommer-Pries CC BY-SA 4.0