Theorems · Definition · category theory

CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion

{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.EssSurj] →
            [F.Full] →
              (X : C) →
                GaloisInsertion (CategoryTheory.Sieve.functorPushforward F) (CategoryTheory.Sieve.functorPullback F)

When F is essentially surjective and full, the Galois connection is a Galois insertion.

Defined in

Mathlib.CategoryTheory.Sites.Sieves

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.EssSurjCategoryTheory.Functor.Full