nLab
full and faithful functor

Contents

Definition

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

F:C(x,y)D(F(x),F(y))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.

Properties

Generalizations

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

Revised on October 5, 2017 11:45:31 by Mike Shulman (76.167.222.204)