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fully faithful functor

(Definition)

Definition 0.1. Let 𝒜 and ℬ be two categories and let F : 𝒜→ℬ be a functor. F is said to be a fully faithful functor if it is an isomorphism on every set Hom(−,−) of morphisms, and that it is essentially surjective if for every object X ∈ℬ, there is some Y ∈𝒜 such that X and F(Y ) are isomorphic.


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See Also: Yoneda lemma

Keywords:  functor, fully faithful, equivalence of categories

Cross-references: surjective, isomorphism, functor, categories
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This is version 4 of fully faithful functor, born on 2009-06-15, modified 2009-06-15.
Object id is 799, canonical name is FullyFaithfulFunctor2.
Accessed 1906 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)

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