ScalingStacks

Example 5.3.2.

We give a few explicit alternative descriptions of \(n\)-surjectivity and \(n\)-faithfulness for low values of \(n\) (and any \(k \geq 0\)).

1. A functor is \((-1)\)-surjective if and only if it is surjective on objects.

2. A functor is \((-1)\)-faithful if and only if it is fully faithful.

3. A functor is \(0\)-surjective if and only if it is surjective on objects and on \(1\)-morphisms.

4. A functor is \(0\)-faithful if and only if the induced functors on hom-categories are fully faithful.