category theory

Contents

Definition

A full and faithful functor is a functor which is both full and faithful. That is, a functor $F\colon C \to D$ from a category $C$ to a category $D$ is called full and faithful if for each pair of objects $x, y \in C$, the function

$F\colon C(x,y) \to D(F(x), F(y))$

between hom sets is bijective. “Full and faithful” is sometimes shortened to “fully faithful” or “ff.” See also full subcategory.

References

• R. Fritsch, D. M. Latch, Homotopy inverses for nerve, Math. Z. 177 (1981), no. 2, 147–179
• Alexandru E. Stanculescu?, Constructing model categories with prescribed fibrant objects, arxiv

Last revised on November 24, 2017 at 09:42:19. See the history of this page for a list of all contributions to it.