category theory, a faithful functor is a functor that is injective on hom-sets, and a full functor is surjective on hom-sets. A functor that has both properties...
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Subcategory (redirect from Full subcategory)
embedding to be a full and faithful functor that is injective on objects. Other authors define a functor to be an embedding if it is faithful and injective on...
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field of topology; see Full set A property of functors in the mathematical field of category theory; see Full and faithful functors Satiety, the absence...
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addition to those functors that delete some of the operations, there are functors that forget some of the axioms. There is a functor from the category...
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between Hom functors is of this form. In other words, the Hom functors give rise to a full and faithful embedding of the category C into the functor category...
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C} . Any functor that is part of an equivalence of categories is essentially surjective. As a partial converse, any full and faithful functor that is essentially...
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Mitchell's embedding theorem (redirect from Full embedding theorem)
commutative) and a full, faithful and exact functor F: A → R-Mod (where the latter denotes the category of all left R-modules). The functor F yields an...
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Equivalence of categories (category Adjoint functors)
{\displaystyle F\dashv G} and both F and G are full and faithful. When adjoint functors F ⊣ G {\displaystyle F\dashv G} are not both full and faithful, then we may...
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Yoneda lemma (redirect from Yoneda functor)
object and only isomorphisms). It allows the embedding of any locally small category into a category of functors (contravariant set-valued functors) defined...
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, h ∈ G {\displaystyle g,h\in \mathbb {G} } and S g {\displaystyle S_{g}} is a full and faithful functor for every g ∈ G {\displaystyle g\in \mathbb {G}...
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