A functor from the category to the category is faithful if for each pair of objects , the function
between hom sets is injective.
More abstractly, we may say a functor is faithful if it is -surjective – or loosely speaking, ‘surjective on equations between given morphisms’.
See also faithful morphism for a generalization to an arbitrary 2-category.
And see 0-truncated morphism for generalization to (∞,1)-categories (see there).
A faithful functor reflects epimorphisms and monomorphisms.
(The simple proof is spelled out for instance at epimorphism.)
basic properties of…
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