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...

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...

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...

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...

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...

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...

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...

{\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...

{\displaystyle u^{*}} is the left adjoint in a pair of adjoint functors and is a full and faithful functor. The category of presheaves over any Q-category is itself...

Presh(D) denotes the category of contravariant functors from D to the category of sets; such a contravariant functor is frequently called a presheaf. Giraud's...