pathterminuspages/math/aboutcontactabout me

2.Full and Faithful

11.06.2020

Contents/Index

1.Definition
@2.Full and Faithful
3.Preserves and Reflects
4.Contra-, Co- and Bivariant
5.Co- and Contravariant Hom Functors

Given two categories $\mathcal{C},\mathcal{D}, and a functor $F : \mathcal{C} \rightarrow \mathcal{D}$, we say that $F$ is

  • full if for every two objects, $A,B$ of $\mathcal{C}$ we have that $$ F : \mathcal{C}(A,B) \rightarrow \mathcal{D}(F\ A,F\ B) $$ is a surjection.
  • faithfull if $F$ is a always injective.
CommentsGuest Name:Comment: