Theorems · Definition · category theory

CategoryTheory.Functor.fullyFaithfulOfCoreflective

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

A coreflective functor is fully faithful.

Defined in: Mathlib.CategoryTheory.Adjunction.Reflective
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Coreflective

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.FullyFaithfulstatement · cited by 87
CategoryTheory.Coreflectivestatement and proof · cited by 9
CategoryTheory.coreflectorAdjunctionproof · cited by 3
CategoryTheory.Adjunction.fullyFaithfulLOfIsIsoUnitproof · cited by 0

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