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Theorems · Theorem · category theory

CategoryTheory.Injective.factorThru.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J X Y : C} [inst_1 : CategoryTheory.Injective J]
  (g g_1 : X ⟶ J),
  g = g_1 →
    ∀ (f f_1 : X ⟶ Y) (e_f : f = f_1) [inst_2 : CategoryTheory.Mono f],
      CategoryTheory.Injective.factorThru g f = CategoryTheory.Injective.factorThru g_1 f_1
Defined in
Mathlib.CategoryTheory.Preadditive.Injective.Basic
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.InjectiveCategoryTheory.Mono
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CategoryTheory.Injective.injective_of_adjoint · cited by 0Injective.injective_of_ad…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Mono · cited by 893CategoryTheory.MonoCategoryTheory.Injective · cited by 70CategoryTheory.InjectiveCategoryTheory.Injective.factorThru · cited by 12Injective.factorThrufactorThru.congr_simpCITED BYCITES

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