Theorems · Definition · category theory

CategoryTheory.Functor.fullyFaithfulOfReflective

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (i : CategoryTheory.Functor D C) → [CategoryTheory.Reflective i] → i.FullyFaithful

A reflective functor is fully faithful.

Defined in: Mathlib.CategoryTheory.Adjunction.Reflective
Cited by: 1 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Reflective

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.FullyFaithfulstatement · cited by 87
CategoryTheory.Reflectivestatement and proof · cited by 27
CategoryTheory.reflectorAdjunctionproof · cited by 10
CategoryTheory.Adjunction.fullyFaithfulROfIsIsoCounitproof · cited by 0

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.bijectionproof · cited by 3
CategoryTheory.bijection_naturalproof · cited by 1
CategoryTheory.cartesianClosedOfReflective'proof · cited by 0