Theorems · Theorem · category theory

CategoryTheory.NormalEpiCategory.preservesMonomorphisms_of_preservesKernels

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteCoproducts C] [CategoryTheory.Limits.HasCokernels C]
  [CategoryTheory.IsNormalEpiCategory C] [CategoryTheory.Limits.HasZeroObject C] {D : Type u_2}
  [inst_6 : CategoryTheory.Category.{v_2, u_2} D] [inst_7 : CategoryTheory.Limits.HasZeroMorphisms D]
  [CategoryTheory.Limits.HasZeroObject D] (F : CategoryTheory.Functor D C) [F.PreservesZeroMorphisms]
  [∀ {X Y : D} (f : X ⟶ Y), CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f 0) F],
  F.PreservesMonomorphisms

Defined in

Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasFiniteCoproductsCategoryTheory.Limits.HasCokernelsCategoryTheory.IsNormalEpiCategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesLimit