 Full and faithful functors: Encyclopedia II - Full and faithful functors - ExamplesThe forgetful functor U : Grp → Set is faithful but neither injective on objects or morphisms. This functor is not full as there are functions between groups which are not group homomorphisms. More generally, for any concrete category the forgetful functor to Set is faithful (but usually not full).
Let F : C → Set be the functor which maps every object in C to the empty set and every morphism to the empty function. Then F i ...
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