Theorems · Definition · category theory

CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [F.Full] →
            [F.Faithful] →
              (X : C) →
                GaloisCoinsertion (CategoryTheory.Sieve.functorPushforward F) (CategoryTheory.Sieve.functorPullback F)

When F is fully faithful, the Galois connection is a Galois coinsertion.

Defined in: Mathlib.CategoryTheory.Sites.Sieves
Cited by: 3 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.Full CategoryTheory.Functor.Faithful

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Cites11

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.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Sievestatement · cited by 552
CategoryTheory.Functor.Fullstatement and proof · cited by 341
CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
CategoryTheory.Sieve.functorPushforwardstatement · cited by 73
CategoryTheory.Sieve.functorPullbackstatement · cited by 49
GaloisCoinsertionstatement · cited by 35
CategoryTheory.Sieve.functor_galoisConnectionproof · cited by 7
GaloisConnection.toGaloisCoinsertionproof · cited by 0

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Sieve.functorPullback_functorPushforward_eqproof · cited by 2
CategoryTheory.Equivalence.isDenseSubsite_functor_of_isCocontinuousproof · cited by 1
CategoryTheory.Functor.pushforward_cover_iff_cover_pullbackproof · cited by 0