Theorems · Definition · category theory

CategoryTheory.Sheaf.functorialLocallySurjectiveInjectiveFactorization

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      {A : Type u'} →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          {FA : A → A → Type u_1} →
            {CA : A → Type w} →
              [inst_2 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)] →
                [inst_3 : CategoryTheory.ConcreteCategory A FA] →
                  [J.WEqualsLocallyBijective A] →
                    CategoryTheory.ConcreteCategory.FunctorialSurjectiveInjectiveFactorizationData A →
                      [CategoryTheory.HasWeakSheafify J A] →
                        (CategoryTheory.Sheaf.locallySurjective J A).FunctorialFactorizationData
                          (CategoryTheory.Sheaf.locallyInjective J A)

Given a functorial surjective/injective factorizations of morphisms in a concrete category A, this is the induced functorial locally surjective/locally injective factorization of morphisms in the category Sheaf J A.

Defined in

Mathlib.CategoryTheory.Sites.EpiMono

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveCategoryTheory.HasWeakSheafify