Theorems · Definition · category theory

CategoryTheory.CoreSmallCategoryOfSet.fullyFaithfulFunctor

{Ω : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (h : CategoryTheory.CoreSmallCategoryOfSet Ω C) → h.functor.FullyFaithful

Given h : CoreSmallCategoryOfSet Ω C, the obvious functor h.smallCategoryOfSet.obj ⥤ C is fully faithful.

Defined in: Mathlib.CategoryTheory.SmallRepresentatives
Cited by: 0 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category

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

DFunLike.coeproof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Set.Elemstatement and proof · cited by 7,166
Equiv.symmproof · cited by 3,681
CategoryTheory.Functor.FullyFaithfulstatement · cited by 87
CategoryTheory.CoreSmallCategoryOfSetstatement and proof · cited by 11
CategoryTheory.SmallCategoryOfSet.objstatement and proof · cited by 10
CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSetstatement and proof · cited by 8
CategoryTheory.CoreSmallCategoryOfSet.homEquivproof · cited by 3
CategoryTheory.CoreSmallCategoryOfSet.functorstatement · cited by 2

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