A functor is surjective on objects if for each object there is an object such that .
This is of course not an invariant notion; the corresponding invariant notion is essentially surjective functor. However, surjective-on-objects functors are sometimes useful when doing strict 2-category theory.
Surjective-on-objects functors are the left class in an orthogonal factorization system on Cat whose right class consists of the injective-on-objects and fully faithful functors.
basic properties of…
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